If a and b are positive real numbers, show that  log_a  b= 1/ log_b  a

Expert Answers
jeew-m eNotes educator| Certified Educator

Let us say;

`y = log_ab`

Now remove log from right side.

`a^y = b`

Now take log on both side with respect to base b.

`log_b(a^y) = log_bb`

`ylog_ba = 1`

`y = 1/(log_ba)`


We know that `y = log_ab`

`log_ab = 1/(log_ba)` answer as required.