Answer
$x= 5 $
Work Step by Step
Given \begin{equation}
\sqrt[4]{5 x-9}=2.
\end{equation} Start by rewriting the radical as a power of fraction and then solve for $x$.
\begin{equation}
\begin{aligned}
\sqrt[4]{5 x-9}&=2\\
\left(5 x-9\right)^{\frac{1}{4}}&= 2\\
\left(\left(5 x-9\right)^{\frac{1}{4}}\right)^3& = \left( 2\right)^4 \\
5 x-9& =16\\
x&= \frac{16+9}{5}\\
& = 5.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\left( 5\cdot 5-9\right)^{\frac{1}{4}}&\stackrel{?}{=}2\\
2& =2\quad \checkmark.
\end{aligned}
\end{equation} The solution is $x= 5 $.
