# How do you write 64^(1/3)=4 in Log form?

Jul 16, 2016

${\log}_{64} 4 = \frac{1}{3}$

#### Explanation:

By definition: ${\log}_{a} b = c \Rightarrow \text{ } {a}^{c} = b$

These two forms, log form and index forms are interchangeable.

#64^(1/3) = 4 is in index form.

$\Rightarrow {\log}_{64} 4 = \frac{1}{3}$

This asks " What index of 64 will give the answer 4?"