# How do you write log_4x=3 in exponential form?

Sep 24, 2016

${\log}_{4} x = 3$ can be written in exponential form as $x = {4}^{3}$

#### Explanation:

${\log}_{a} b = m$ can be written in exponential form as ${a}^{m} = b$

Hence ${\log}_{4} x = 3$ can be written in exponential form as $x = {4}^{3}$

Sep 24, 2016

${\log}_{a} b = c \text{ "hArr" } {a}^{c} = b$

#### Explanation:

Log form and exponential form are two different ways of saying the same thing.

They are inter-changeable.... neither form is better than the other, but one might be more useful than the other in a particular question.

${\log}_{a} b = c \text{ "hArr" } {a}^{c} = b$

An easy way to convert between the form is to remember:

"The base stays the base and the other two change around"

Here are two examples:

${\log}_{10} 100 = 2 \text{ "hArr " } {10}^{2} = 100$

${\log}_{3} 81 = 4 \text{ "hArr " } {3}^{4} = 81$

In this question:

${\log}_{4} x = 3 \text{ "hArr " } {4}^{3} = x$

$x = 64$