Answer
$\pm 1.6212$
Work Step by Step
We need to take natural log of both sides , then the given expression can be written as:
$\ln e^{x^4}=\ln 100 $
Apply logarithmic property : $\log a^ b=b \log a$ and $\ln e^a= a$
$x^4 =\ln 100$
Now, we will evaluate the result for $x$ by using calculator.
Therefore, our answer is: $x =\pm \sqrt [4] {\ln 100}=\pm 1.6212$