proof of logarithmic property $ a^{\log_{a}{b}}=b$

Question

I don't know how to show that $\displaystyle a^{\log_{a}{b}}=b$

Can anyone give a hint?

That's a possible definition of $\log _ab$. – Git Gud Mar 06 '14 at 18:14 — Git Gud, Mar 06 '14 at 18:14

lab bhattacharjee · Accepted Answer · 2014-03-06T18:16:50.847

3

Let $\displaystyle\log_ab=c$

$\displaystyle\iff a^c=b$ (from the definition of logarithm)

Replace the value of $c$

edited Mar 06 '14 at 18:16

answered Mar 06 '14 at 18:11

lab bhattacharjee

score 0 · Answer 2 · edited Mar 06 '14 at 18:45

0

As commented by Git Gud, this is actually a definition of the logarithm of $b$ with base $a$.

edited Mar 06 '14 at 18:45

MPW

answered Mar 06 '14 at 18:22

2 Answers2