Answer
$x = -\dfrac{1}{4}$
Work Step by Step
Note that $\dfrac{1}{\sqrt{2}} = \dfrac{1}{2^{\frac{1}{2}}}=2^{-\frac{1}{2}}$.
Thus, the given expression is equivalent to:
$4^x=2^{-\frac{1}{2}}$
Write $4$ as $2^2$ to obtain:
$(2^2)^x=2^{-\frac{1}{2}}$
Use the rule $(a^m)^n=a^{mn}$ to obtain:
$2^{2x} = 2^{-\frac{1}{2}}$
Use the rule $a^m=a^n \longrightarrow m=n$ to obtain:
$2x = -\dfrac{1}{2}$
Divide 2 on both sides of the equation to obtain:
$x = -\dfrac{1}{4}$
