Question

Rewrite 34 = 81 in logarithmic form.

Answer 1

Answer:

$log_3(81) = 4$

Step-by-step 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

$\frac{4log3}{log3} = \frac{log81}{log3}$

$4 = \frac{log81}{log3}$

From laws of logarithm;

$\frac{loga}{logb} = log{_b}(a)$

So;

$4 = \frac{log81}{log3}$ becomes

$4 = log_3(81)$

$log_3(81) = 4$

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