Answer
$3$
Work Step by Step
Use the definition $\log_b {x} = y \longleftrightarrow b^{y} = x$, to write an exponential equation.
In this exercise, the base $b$ is $4$, $y$ is the exponent, and $x$ is $64$:
Let $y=\log_4{64}$
Then, use the definition to obtain:
$4^{y} = 64$
Rewrite terms so that they both have the same base:
$4^{y} = 4^3$
If two numbers having the same base are equal, that means that their exponents are also the same, so set the exponents equal to one another to solve for $y$:
$y = 3$
Therefore, $\log_4{64}=3$.
