Solve the logarithmic equation.
\[
\log _{4} x=4
\]
\[
x=\square
\]
(Simplify your answer. Type an exact answer, using $e$ as needed.)

Answer

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Answer

The solution to the logarithmic equation $\log _{4} x=4$ is $x=\boxed{256}$.

Steps

Step 1 ：The logarithmic equation is in the form $\log_b a = n$, which can be rewritten in exponential form as $b^n = a$. In this case, $b$ is 4, $n$ is 4, and $a$ is $x$. So, we can rewrite the equation as $4^4 = x$.

Step 2 ：$b = 4$

Step 3 ：$n = 4$

Step 4 ：$x = 256.0$

Step 5 ：The solution to the logarithmic equation $\log _{4} x=4$ is $x=\boxed{256}$.

Solve the logarithmic equation.\[\log _{4} x=4\]\[x=\square\](Simplify your answer. Type an exact answer, using $e$ as needed.)

Answer

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Solve the logarithmic equation.
\[
\log _{4} x=4
\]
\[
x=\square
\]
(Simplify your answer. Type an exact answer, using $e$ as needed.)