Answer
$\dfrac{3}{4}$
Work Step by Step
Let $y=\log_{16}{8}$
Use the definition of logarithm $\log_b {x} = y \longleftrightarrow b^{y} = x$ to write an exponential equation.
In this exercise, the base $b$ is $16$, $y$ is the exponent, and $x$ is $8$:
$16^{y} = 8$
Since $16=2^4$ and $8=2^3$, the equation above is equivalent to:
$(2^{4})^{y} = 2^{3}$
When raising a power to a power, multiply the exponents, keeping the base as-is:
$2^{4y} = 2^{3}$
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 $y$:
$4y = 3$
Divide both sides by $4$ to solve for $y$:
$y = \frac{3}{4}$
Therefore, $\log_{16}{8}=\frac{3}{4}$.
