The change of base formula allows us to compute any base logarithms from another one. That is :
So you plug in your values : you have , and you want to be able to calculate this with your calculator. Your calculator (hopefully) has a "log" button, so we'll use this one. It's the decimal logarithm, so . And we want to compute . So :
And this gives exactly
This can be verified easily : it is equivalent to saying that , which is true (you can check)
You wouldn't. You would use the definition of "logarithm to base a" which is that it is the "inverse function" to . The logarithm is defined by "if then ".
That's all you need.
Learn the definitions first!This is simply review and i never really learned how to do it.
Prove it, in addition to simply giving a wrong calculation, seems to think you were trying to solve but the solution to that is which is your first equation. I assume you are really asking how to go from one equation to the other.
If you are really asking how to write in terms your calculator can handle,use the fact that is then so that where "log" can be either base 10 (common log) or base e (natural log), both of which should be on your calculator.