Tryimg to understand this logarithmic identity

[mileena]

(I know the title contains a typo, but I can't edit it!)

I'm trying to understand and/or prove this identity:

b^log_bx = x

I've inserted numbers, and it does work, but I just don't seem to understand why. I mean, some identities are obvious, like:

log_b b^x = x

since b^x = b^x

but I can't make any sense of the top one.

Also, I'm sorry for posting a lot. This is my third thread today!

 

[micromass]

The logarithm of $x$ is the unique number $n$ such that $b^n =x$, right? So $n=\log_b(x)$. Thus $b^{\log_b(x)}=b^n = x$.

 

[mileena]

Well, now that you wrote it micromass, I guess it seems kind of simple. I'm going to print this one out so I can study it some more!