Answer
$\dfrac{3}{2}$
Work Step by Step
Let $\log_4{8}=y$.
Use the definition of logarithm $\color{blue}{\log_b {x} = y\longleftrightarrow b^{y} = x}$ to write the equation above in exponential form:
$$4^{y} = 8$$
Rewrite terms so that they both have the same base (note that $4=2^2$ while $8=2^3$):
$$(2^{2})^{y} = 2^{3}$$
Raising a power to a power means we multiply the exponents (use the rule $\left(a^m\right)^n=a^{mn}$):
$$2^{2y}=2^3$$
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 $x$:
$$2y = 3$$
Divide both sides by $2$ to solve for $y$:
$$y = \frac{3}{2}$$
Therefore, $\log_4{8}=\dfrac{3}{2}$.
