Answer
$ 4$.
Work Step by Step
The given functions are
$f(x)=(9x+2)^{\frac{1}{4}}$ and $g(x)=(5x+18)^{\frac{1}{4}}$
Equate both functions
$\Rightarrow f(x)=g(x)$
$\Rightarrow (9x+2)^{\frac{1}{4}}=(5x+18)^{\frac{1}{4}}$
Raise the power to $4$ on both sides.
$\Rightarrow \left [(9x+2)^{\frac{1}{4}}\right ]^4=\left [(5x+18)^{\frac{1}{4}}\right ]^4$
Multiply exponents on both sides.
$\Rightarrow 9x+2=5x+18$
Add $-5x-2$ to both sides.
$\Rightarrow 9x+2-5x-2=5x+18-5x-2$
Simplify.
$\Rightarrow 4x=16$
Divide both sides by $4$.
$\Rightarrow \frac{4x}{4}=\frac{16}{4}$
Simplify.
$\Rightarrow x=4$.
