What is the solution to $$ 4^{\log _{4}(x+8)}=4^{2} ? $$ $$ \begin{array}{l}x=-8 \ x=-4 \ x=4 \ x=8\end{array} $$ $$ \begin{array}{l}x \ x\end{array} $$

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Solve the equation $$ 4^{\log _{4}(x+8)}=4^{2} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$4^{\log_{4}{\left(x+8\right)}}=4^{2}$$
- step1: Find the domain:
  $$4^{\log_{4}{\left(x+8\right)}}=4^{2},x>-8$$
- step2: Set the exponents equal:
  $$\log_{4}{\left(x+8\right)}=2$$
- step3: Convert the logarithm into exponential form:
  $$x+8=4^{2}$$
- step4: Evaluate the power:
  $$x+8=16$$
- step5: Move the constant to the right side:
  $$x=16-8$$
- step6: Subtract the numbers:
  $$x=8$$
- step7: Check if the solution is in the defined range:
  $$x=8,x>-8$$
- step8: Find the intersection:
  $$x=8$$
The solution to the equation $$4^{\log _{4}(x+8)}=4^{2}$$ is $$x=8$$.
$$ x=8 $$.

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