# How do you write 3log_(4)16=2 in exponential form?

Sep 30, 2015

${4}^{2} = 16$

#### Explanation:

According to the definition of log:
$y = {\log}_{b} x$ is equivalent to ${b}^{y} = x$

So we have:
$3 {\log}_{4} \left(16\right) = 2$
${\log}_{4} \left({16}^{3}\right) = 2$

Compare what we have to the definition of log:
$y = 2$
$b = 4$
$x = {16}^{3}$

Therefore:
${4}^{2} = {16}^{3}$

However, ${4}^{2}$ is definitely not equal to ${16}^{3}$. I think you probably meant "${\log}_{4} \left(16\right) = 2$" instead, which would have resulted to the answer $\textcolor{b l u e}{{4}^{2} = 16}$.