\(a^log_ab=b\)

a^log_ab=b

Saw it in a textbook (Revision) How does it work ?

Guest Sep 16, 2019

#1**+2 **

a^ ( log_{a }b) = b (1)

I'll admit that when I first saw this in Algebra it was a little tough to see

Let's prove this is true :

Take the log of both sides

log a ^ (log_{a} b) = log b and by a log property we have

( log_{a} b) * log a = log b divide both sides by log a

log_{a} b = log b /log a by the change-of-base rule for logs we can write

log b / log a = log b / log a

Since this is an identity....then so is (1)

CPhill Sep 16, 2019