# How do you write the equation log_8 (4)=2/3 in exponential form?

Jan 4, 2017

$4 = {8}^{\frac{2}{3}}$

#### Explanation:

If ${\log}_{b} a = k$, its inverse is $a = {b}^{k}$.

Here, the inverse of ${\log}_{8} 4 = \frac{2}{3}$, the inverse is $4 = {8}^{\frac{2}{3}}$.

Some more examples:

RELATION INVERSE (for the same relation)

$y = \ln x \to x = {e}^{y}$

$y = \log x \to x = {10}^{y}$

$2 = {\log}_{16} 256 \to 256 = {16}^{2}$