Question

Rewrite 34 = 81 in logarithmic form.

Answer 1

`log_3(81) = 4`

Explanation:

Given

`3^4 = 81`

Required

Rewrite in logarithmic form

We start by taking log of both sides

`3^4 = 81`

`log3^4 = log81`

From laws of logarithm;

`loga^b = b\log(a)`

So;
`log3^4 = log81` becomes

`4log3 = log81`

Divide both sided by log3

`(4log3)/(log3) = (log81)/(log3)`

`4 = (log81)/(log3)`

From laws of logarithm;

`(loga)/(logb) = log{_b}(a)`

So;

`4 = (log81)/(log3)` becomes

`4 = log_3(81)`

`log_3(81) = 4`

Hence,
`3^4 = 81` in logarithm form is
`log_3(81) = 4`