# How do you write log_x(64)=3 in exponential form?

May 9, 2018

${x}^{3} = 64$

#### Explanation:

$\text{using the "color(blue)"law of logarithms}$

•color(white)(x)log_b x=nhArrx=b^n

$\text{here "x=64,b=x" and } n = 3$

$\Rightarrow {\log}_{x} 64 = 3 \Rightarrow {x}^{3} = 64$

May 9, 2018

$64 = {4}^{3}$

#### Explanation:

${\log}_{x} \left(64\right) = 3$

${\log}_{x} \left({4}^{3}\right) = 3$

$3 {\log}_{x} 4 = 3 \to x = 4$

Hence, we can express the identity in exponential form as: $64 = {4}^{3}$