Lớp 12: Các phương pháp giải phương trình mũ p1 #toan12

The first method for exponential equations is to bring them to the same base the idea of this method is as follows If we now have A multiplied by f(x) equal to A multiplied by g(x) then we can immediately conclude that f equals g In the second case where A raised to the power of fx equals b we can conclude that f equals the logarithm base a of b The first example is 2 cubed times 5 equals the logarithm base 2 of 8 times 32 What do you think What should we do now Now I will convert it to base 2 Why did I think of the idea of converting to base 2 Because it already has a base 2 available Does the 8 x 32 base convert to 2 as well So now I remember this 2 cubed is 2 to the power of 3 What power of 2 is octal Is 2 cubed correct Well I remember that A's exponent m is very large en by A raised to the power of m over Then the base 2 Base The second part of 8 is it that I consider it the second part of 23 What is it equal to 2 cubed times 2 equals Is that right 23 x 2 Then I think this one is 23 x 2 But 32 is 2 to the power of what 2 to the power of 5 times 5 equals 2 to the power of 3 times 5 by 2 to the power of I also know that A to the power of m divided by A to the power of n How do we do it when it's divided I take the hat from above Exponent in the denominator Then how much is it How much is Revision It is a hat minus 7 times 2 Yes 32 multiplied by 5 So up to this point we will ge You get the base then Then you just need to make the exponents equal Once you get the base you just need to make the exponents equal So what you get is 3 times 5 by 7 x 2 I'll take it then By 1 x 2 That's it _STRING This is an action that brings it back to the same base But this base is a very beautiful base Now we add another one Another example also leads to the same base number But the base number will be more complex We rank the second scenario Dear when we encounter this number We will ask the question Asking the question The number 3 x 2 x 2 is 2 times 1 What's the connection What's the relationship It must have a relationship If it doesn't have a relationship we can't process it Did anyone notice The relationship is direct and indirect which is 3 x 2 x 2 and 2 x 1 has no direct relationship but has an indirect relationship This you see in water 9 then remember more That is how we have this analysis 3 x 2 x 2 3 times 1 3 times 2 times 2 Do you remember the code2 x 2 x 2 1 x 12x 1 x 1 A normal B normal 2 x 2 x 2 and 9 x 2 x 2 are all normal That is definitely the way So we can handle this by meaning 2 x 2 x 1 all is normal That is it This is your turn It is by 2 x 2 x 2 All is normal That is 2 x 2 x 2 So this one then You still remember the other day We said that when we met this friend If it's a Tang family member remember its clan rules What is its clan rule Dear if it's someone with a clan rule that's great right The secret is that you can share many things Not saying everything but sharing many things For you is that the right way Then this A plus B I talked to a friend who is that friend A letter B And in math this is called a conjugate expression Conjugate expression The plus sign of the set goes together And it is as it is it will become one Korean yes Then when that The expression of this Can two characters with one meaning is can two characters one That is these two people are The combined expression of each other Then I'll try multiplying again to see what happens I'll multiply again Then you will see that 2 plus 1 If now we multiply by 2 and 1 I will find out something very fun How much is it Just 1 According to the standard it's 2 cans of 1 can of beer It's exactly 1 Then like the other day we did It's about talking if two AB numbers are multiplied then two 1s then it can be imagined that this number is equal to the other number to the power of 1 Is that right This number is equal to that number raised to the power of 1 Why is that It's because The price range is approximately betwee Is A equal to 1 over B 1 on B is written differently It is B with a superscript 1 So the 2 ones you have It seems like organiztion 2 A regular plus one is a plus one with the number one That is a plus one with the number one So what happens next This person we will have is a plus one with the number one 3 plus 2 is 5 this is the one This is the one you have This is the 2nd hat So what is the name of your little rat Then this one we will write like this okay Can 2 plus 1 All normal Normal as that hat goes up We will have the formula always It is 2 plus 3 What is that formula That is A to the power of m If all to the power of n Then it will be A to the power of m Multiply n Do you remember Should have been like this right This hat is here 2 times 3 But anyway I'll just go back Use this hat and go back always What did this person turn into Can 2 digits 1 Become plus 1 power of digit 1 okay Then All together power of x digit 1 Together x squared 1 But we can be That is once again this formula Then it becomes x squared 1 multiplied by n So we changed it right away He is a 2 plus 1 type of person with a X-shaped head and a 1 That is it Then is now the time we have two identical sets together Do we have two identical sets now Then all I need to do is make the hats equal right It's equivalent now X equals This way you can receive The letter x is converted to the number 5 6 is converted to the number 5 and x is equal to 1 It's certain There are some numbers It appears and then I just count it There are some numbers that have not appeared yet It's certain that there is 1 number Let's look at another example Example How do we handle the issue In the form of a process we have one division actio The movement is divided That is Be careful about one thing First A is positive for all x Of course A must be equal to 1 The base is greater than 1 In short I understand The exponent is always positive Then then I urge you to divide by the friend Then at that time It will be equivalent to dividing by 4 times x This is 3 This is 8 This is 8 x Divided by 4 x 8 x 4 points 8 x 4 points 2 points We have a tradition tha The tip of A is x and the tip of B is x Usually chosen What is this worth Okay I'll switch to x x Divide by 4 x Then I divide by 3 I divide by 3 3 times 3 needles x 2 times 1.3 If x equals b then we have x equals what the logarithm base a of b let's use this notation for now Equivalent to x equals the logarithm base 2 of 1 over 3 The second method is to reduce it to a product The equation is reduced to a product which is a basic method If the product of two numbers is zero then each of them is zero 10 plus 5 equals 5 plus 1 plus 2 First 1 plus a plus b equals a plus b The model is 1 plus the product equals the sum Then when doing math they fold it like this fold 1 with a fold a b with b Then what will it get Will it become this letter "a" Is this the correct placement for the letter B Is this the correct "1" character Is it correct I'll move the b to a then put b out is there still an a letter 1 This is 1 What about 1 a letter and a 1 letter They are the same it's just that they hide each other What will we get then It's the same I'll put an "a" outside So now what This doesn't cause anything we just play it like one This place is covered in signs so I'll just play around and fix the signs again That means it will directly change the letter a into the letter b By 0 Not just the nose not just the logo not just the usual design not just the usual armor how does it also appear Then of course it would be a or b right That's the first type the first situation isn't it The second situation is a o tộc b v by a v tribe b u That is to say There are 4 factors you know a o b u b It has a loop around it But there is one segment that is each tip v Each row has 2 people Each row has 3 people So in total there are 4 people When there are these 4 people What is their skill That is they are putting it together You look at them putting it together Are you allowed to pair up with anyone Then the connection is made like this What does it lead to It is equivalent to This is the two of them going together I placed him outside U character V Now I'll transfer this person to you does it have a "u" letter Here I'm transferring you to this person One sustainable thing is that this is the letter V this is the letter U That's great Now I meet the letters u and v You It will become the letter V and not the letter A with B I encountered the letter V It also means or is v by u or smooth luster If you come across a model like this we can meet up A third situation I will encounter this word is when I meet it A plus B times C equals A times C plus B This door is the special character of the character "chiên " then I also combine it like that we combine it like this A plus B equals what This is equivalentード to you putting a out there is there a "c" correct Same thing and not뜩 The vector of A plus B Multiply A by B and do no Please pay attention here is the sum here is the total then according to theorem known by children this is the total of two meanings one This is the product of two meanings 1 according to the known theorem this is the sum of two meanings then the sum of two meanings is two meanings are the letter A 4 means 2 meanings will have the character "T" this is the letter "A" 2 meanings is the character "T" and "B" means the character "T" it will be this still prove it prove it then I remember fold it up Here it is will be the brand name from A T from B T Adding A and B to zero then this person will meet the name appearing outside will be the name of A and this person meets Is that correct Then now come here when I meet person A outside then there will be person B D In the end you will see that although the details of each of these elements are different overall it is the same 1 2 3 4 Four friends you know I will remember this number Then when we call the problem 1 2 3 4 we can see that we can be different remember that and then we'll move on This is first First beauty is 5 x of 1 This is number 10 I know it is number 10 It is equal to 2 x 5 So 10 needles x is equal to what equal to 2 needles x multiplied by 5 needles x is that correct so we have the following transformation 2 needles x 5 needles total 5 en you still remember about the total of the exponents that is 2 raised to the power of x y equals 2 raised to the power of x multiplied by 2 raised to the power of y right 2 raised to the power of x multiplied by 2 raised to the power of y so that is the case This article 5 to the power of x times 5 to the power of y 5 to the power of x multiplied by 5 to the power of x 5 to the power of x multiplied by 5 to the power of y which of the four friends is it Now we will pair up Pair this one with that one Then pair this one with that one What do these two have in common 5 of these needles and these two just keep going together Go ahead and pair them up or whatever we know is that four of them go together then just pair them up and it will be successful 5 times 5 is 25 5 times 5 is 25 from 5 why is that here I put these two together Should we now put 5 outside There are 2 here As for this number 5 move it here Move it right below like Ten minus two or not I will switch here with here Then this person is not equivalent to now I put 2 minus 5 outside will be 5 needles subtracting the self of this person and this person is opposite must hide it is opposite Unlike usual when I 아니 라 2 minus 5 wherever I change direction from minus it will be 5 minus 1 by 0 and leads to two cases the first is 2 x 2 equals 5 Monday is 5 times 1 5 times 1 is 5 equals 0 is that correct because Which number is 0 nose also equals 1 nose 5 nose also equals 0 nose 1 then x equals 0 and the one above follows the formula above x is equal to log base 2 of 5 so we get the solution to this problem is Weak points are combined to create a middle section and then comes the final step leading on Then the children try it out problem number 2 24 needles x 12 2 tips x x 2 x 3 x 1 First we can think of it like this the 24th edition 24 is equal to 3 times 8 right The 24 needle pattern is equal to 2 needles times 18 needles Is that correct e number 12 en I can think of it as 2 times 6 or 3 times 4 e 2 x 7 x 2 model Then I can think of it as 2 times 7 plus 242 but 247 should also be 23 times 8 right 8 pieces Four correct right then the 3 x 1 sheet the students can think it's 3 needles x 3 needles 1 So we decided on 3 x 3 needle points then now we choose which acupuncture point to use But the number 24 nose I'll just leave it as 3 noses x x 8 noses again Keep it as is there's 12 left This one add 4 with 8 needles right Here 2 needles 2 is 4 There are 2 needles of 3x that is 8 needles With 3 so with 3 arrows So do you notice that this person is going together or this person is going together is okay Hurry up everyone hurry up there's nothing coming out Here I ordered 8 needles okay Eight stitches here are three stitches by four right Are you moving this one to the front and this one to the back making 8 Xs So if there are 3 Xs then the number is 4 right There is one more shot now we place three outside here is the part with four numbers for three shots 12 this 12 is If I put 3 outside then there's also 4 left right The three needles I placed outside are now three needles x But the number is reduced because I moved them over here These two are similar but not the same they should be similar So I still put one outside Then I'll put three outside 3 times 4 is 12 So now it will be 6 times and it's 3 times here Is that right So now there are two cases that is 3 x and 4 Then what is this case x and how many Chapter 2 verse 3 of 4 There are 8 groups of 3 which is 8 x 3 Then we will get x gold Rô 2 for the 8 of 4 We will look at one example with 3 Give me two examples each of the positive and negative sides Example 4: x is a vector Three needles x Total five needles x Multiply by 2 times x Add 15 times x Is it still there X for 8 shots X You have 8 bullets I still realize that it doesn't matter what you meet In short I have an idea That's just putting it all together to create a common image Just having such an idea is enough That will be successful Just having an idea is enough Combine to create a shared image That is success Creating a couple produces a human image Click on the Here we have 4 stitches 3 stitches x Multiply by 12 stitches x 5 stitches x Fifteen x equals fifteen x then x is five x multiplied by three x 15 divided by 3 is 5 Multiply by 3 Just multiply these two Then We have 1 straight idea Before we said 4 x tips 4 x tips means 2 x tips 2 x tips are all normal 2 tips x 2 tips x all is fine So that means you two have a shared idea What is it That is two x's So we place two x's outside Two x's Multiply by Two x's times two x's Multiply 5 times 5 times outside 2 needles x 3 needles Then the general idea of mine is 2 needles x 3 needles Multiply 2 times 5 times 0 Actually here we have this type we have one type that is type 4 the regular T this is T this is the regular T Together with AB Then here we will get is: First row is:2x x 3 x x 0 We have 3 shots 3 shots 0 So remember that if a times x equals b times x then we can conclude that x equals zero So in this fold we summarize x as 0 For this number 1 we need to restate that this number 1 is x coming from 3 with the entire 0 It has the same base x equals 0 So remember from now on if a person is equal to 1 then you take it as 0 If a person has a nose that is equal to 1 then you take x as 0 And later remember that if a times x equals b times x and a and b are different then we conclude that x equals 0 Then similarly that equation 2 sin x equals 5 sin x is the same right Then we can also conclude that x equals 0 And this leads to the equation which means x equals 0 Sure We move to the third method The coating brings the equation to the surface These are the types of problems First example The base 2 logarithm of x Multiply the base 2 logarithm of 2x By 12 For example this equation Just a study of letters Log of study of letters 3x plus 1 Multiply 3 squared by x equals 3 squared times x It adds up to 28 With this equation I will separate it into parts Multiply 3 to the power of x right 3 squared can be 9 Divide by 3 to the power of x Is that correct Because we have the formula of A to the power of x times y Then A to the power of x divided by A to the power of y So this part is divided by 3 to the power of x Then 3 squared is 9 And so now I will set the cover part to 3 to the power of x Look at this note All exponential functions are positive As just noted and previously 2 to the power x is always positive 1 to the power x With a hat 1 hat x Now we have a new cover It turns out to add just T Add 9 to T EqualsBackColor 28 Is that right These two are the same So I'll set it again Now I get this equation Now I take T I take T and multiply by 2 seats Then is 3T equal to 1 method Add 9 By 28T Here I am multiplying T by 2 seats o source language words proper nouns preserved punctuation correct Also the translation should be natural Let me adjust for fluency This one turned into an 8T Ren T into two seats This is the quadratic equation then Quadratic equation Then I can be 1 for calculation or maybe it's a mistake What is T equal to How much is T One third of a u Whoever has T equal to one third Then T equals three haps Batch 9-9 One third to nine Then 9 Then T is 1/3 What is T T is 3 needles 3 needles and 1/3 right One third is three parts right This shows that x equals x X is tone 1 It's 9 o' clock I'll show 3 arrows at 9 9 is 3 squared so x equals 2 So we have found 2 solutions Those are the negative solution 1 equals solution 2 That is the main part The rest is secondary It's just that we often see very similar elements Then we just express our opinion The second one is 27 needles From 3 needles 2 times total 1 Two plus zero equals two Do you have any ideas Do you know that 27 multiplied by 3 is 81 3 multiplied by 3 times all the other numbers So we acknowledge that this is 3 multiplied by 3 This one is analyzed as 3 shots 1 and multiplied by 3 shots 2 x Two equals zero We have a note that three arrows three x This person is three arrows x all arrows three right There are 3 pieces of 2 3 needles 2 x This one is 3 needles x all 3 needles Right So they all go back to 3 needles x right So we can write this equation like this 3 shots x All 3 shots 3 multiplied by 3 equals 9 all 3 times 3 equals 9 Two equals zero That means we will now hide the second What is the building made of 3 roots x Build positive Then we get a new equation Two equals zero This is an unbeatable equation Equation 3 Equation 3 is Task T1 When there is task T1 Then we can think like this If T is 1 its factor will be equation 1 Is that right Now we will build a positive Window Also they becauseWhether NgceğizRight But in this section we will add 2T add 2T of sugar Because later I will put the 2T outside Once it's out it will have a first type T that matches its surgery What else are we going to do next Then because there's no 2T above we just have 2T right Then add 2 like this Then I put my T outside To be the first T From 2T with T first From 2 multiplied by T first Equal deep That would be written here and it would become First T Multiply by T squared From 2T From 2 by depth My equation is T round 1 Round 1 means 3 people times round 1 That means 3 people times round 1 It means deep round x The second equation is T squared minus 2T plus 2 equals zero Then we must have two solutions which are T equals 1 plus or minus i 1 plus 3 equals 4 Or a single character weighs three but if T weighs three then it's out One scale has three types because when it is negative it is excluded Because T is positive Therefore the result here is three people plus one round plus three scales Then where does that lead us X is the logo Base 3 of 1 plus 3 pounds Is it all bad In conclusion this method is just imagining that you will bring it back the hidden part bringing it back to the algebraic equation we just do it normally Example 3 That is 4 circles x 1 character x 4 circles x 1 character x 2 circles x 1 character x 2 circles x 1 character If we put them together the lover would be very charming and very sweet Then Actually it's related to this matter If you ask about A there are two people X Then the 2 words x 1 is 1 out of 2 because it relates to 2 words x 1 circle 1 and 4 words x Now it will become A4 4 characters x Then it will become 1 on A4 So in reality it is It will be in the form of A squared weight on A squared And 1 out of 2 Then what did you discover I discovered that A squared weight on A squared If we add more 2 people x 1 round on A Monday Then it creates Isn't that right Then this person must be the A heavy opponent on A square Tuesday By A 1 out of 2 Actually this is related to the Transformation of Frugality Just like x squared plus y squared Now we add two more y's Then it becomes clear So it's definitely stuck again I'm lost again with A in the middle of A Then it follows that now I have The second power of T And T This is the equation equal to 2 But my T is positive T This equation is equal to 2 I have to be normal Then I will discover there is 1 point First floor of the sunny building That positive point is Point T with a value of 2 T equals 2 Now put it into A at position 1 on A T equals 2 Explain this equation Because of the common denominator = Prime It will lead to the single point goal This is a goal in the first half Being in the first position means we will have two arrows left By 1 That is T equals 0 Then there are a few more methods but today I'm also tired We'll finish early today I'll stop here okay Then I will send back this video Thank you