A Nice Exponential Problem |Algebra|Exponents

Celebrating our 20K subscribers today — I'm so grateful, thank you so much for your support. Thank you so much to the 20,000 amazing subscribers—that's a huge milestone! Okay, thank you, I'm so happy. And I'm truly grateful. Now, let's celebrate that with this specific question we have on the board. It's an easy one, yes, I know. I don't want us to solve something difficult now. Today's celebration day celebration time Don't mind me, don't mind me. So let's solve what we have on the board now. When you look at this What can you see? It's actually easy. So this question is under exponents. Let's go ahead and Put them in the same base; that's the first thing we're supposed to do, so we have two to the power The square root of x equals eight can be expressed as two to the power of three. raised to the power of x, okay, so we have two raised to the power of the square root of x is equal to two now when you have a raised to the power of m and this is also raised to the Okay, this can be expressed as a raised to the power of m times n. Okay, so we are going to do that. Here, three times x will give us three x. Now, whenever you're solving any question on that exponents; whenever you have the same base, you equate the powers; it means that the so we can now write that root x is equal to three x Using the same approach, we can now write that the square root of x is equal to three x. to remove a square root of anything, just square it; if you have a cube root, then Remove the cube root and just cube it, so we are going to square both sides of this equation to eliminate this. square root sign, so we are going to have square root of x squared, okay, is equal to three x squared Okay, now this square will cancel this square root, so we have x equals These two are the squares for both three and x, okay? So it's going to be three to the power of two. which is nine and x to the power of two, which is x squared, so let's bring this to the other side of the equation, so we have x minus nine x squared is equal to zero. Now, what do they have in common? They have x, so let's factor out x now. x divided by x will give us one. nine x squared divided by x will give us nine x, which is equal to zero. Now this simply means that x is equal to zero, so this becomes the first value of our x. Or, one minus nine x is equal to Zero. Okay, so if we continue solving, we have established the value of our x. Let's focus on this one now. This one says that one minus nine x is equal to zero, okay. That means one is equal to this, which we move to the other side to become nine x. And since we are looking for the value of x, let's divide both sides by nine so that nine can cancel. so we have divided by nine divided by nine, so we have that the second value of x It is going to be one over nine, so we have the first value of x to be zero; thus, these are the two values. of x, don't forget to subscribe and to turn on your notification bell if this is the first time You are seeing this face