Answer
$\left\{\dfrac{3}{2}\right\}$
Work Step by Step
Using exponents, the given equation, $
\log_2 \sqrt{8}=x
$, is equivalent to
\begin{align*}
\log_2 \sqrt{2^3}&=x
\\
\log_2 \left(2^3\right)^{1/2}&=x
\\
\log_2 2^{3/2}&=x
.\end{align*}
Using the properties of logarithms, the equation above is equivalent to
\begin{align*}
\dfrac{3}{2}\log_2 2&=x
&(\text{use }\log_b x^y=y\log_b x)
\\\\
\dfrac{3}{2}(1)&=x
\\\\
\dfrac{3}{2}&=x
.\end{align*}
Hence, the solution set of the equation $
\log_2 \sqrt{8}=x
$ is $
\left\{\dfrac{3}{2}\right\}
$.
