How do I prove that $a^{\log_a(b)}=b$?

Question

All in the title basically. Not sure how to prove $a^{\log_a(b)}=b$.

Don't know how to use the rules to get that.

That's the standard definition of $\log_a b$. If you want to use a different definition, you should specify which. — lulu, Jan 18 '20 at 15:11

score 0 · Answer 1 · answered Jan 18 '20 at 15:23

0

The definition of logarithm will do

You may also use the following argument

Let $a^x=b$ and solve for $x$

Take logarithm and you get $\log a^x=\log b$

$$x \log a =\log b$$

$$x=\frac {\log b}{\log a} =\log _a b$$

answered Jan 18 '20 at 15:23

1 Answers1