Logarithmen mit fremden Basen | Mathe by Daniel Jung

Logarithms of foreign bases. Why foreign bases? You come from the base 10. A simple example. 10 raised to how much is equal to 100. You can of course do it in your head. x is equal to 2. Why? 10 raised to 2 would be 10 times 10 equals 100. But it is important to rewrite here. If we had x equals logarithm 100 to the base 10. In the complete calculation you would then write lg100 divided by lg10. What is lg? log to the base 10 equals lg. You would get two out accordingly. Even if you type in lg100, because lg10 would be the logarithm again from 10 to the base 10. Because lg100 is 1, you divide by 1 and you get two out. But what if the base 8, 7, 5 or whatever? A little math now. How could you rewrite 8? 8 equals, but with the base 10. So 10 raised to how much is equal to 8. And why is that lg8? You ask yourself now. 10 raised to how much is equal to 8. Then we would have x is equal to the logarithm of 8 to the base 10. And that would be lg8. Now you can use this expression for 8. Then we would have 10 raised to lg8 for 8 raised to x equals 95. Potentials are potentiated. The basic requirement here is to calculate with potentials. Potential laws. Potentials are potentiated by multiplying the exponents. So 10 raised to lg8 times x, so that it becomes clear, is equal to 95. So what do we have now? Now we have to ask ourselves. 10 raised to this here, so lg8 times x is 95. And what value do we need here now? What must lg8 times x be? That must be lg95. I always make brackets around it. Because 10 raised to how much? This is equal to 95. That would be 10 raised to lg95. You can pause again and then look here. That's why I can say lg8 times x is equal to lg95. And here we can convert lg95 to lg8. This will also continue when you come to the topic of the special exponential function with the base e and then come to the natural logarithm. I can also do that with the natural logarithm. But that's why you can calculate x here. And that's how it works. I hope that could help. Otherwise, go to the comments. I still refer to the playlist, where there is more about logarithms. Otherwise, math vocabulary recognized, danger banned.