Solve for x
x=\ln(2)\approx 0.693147181
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e^{4x}=16
Use the rules of exponents and logarithms to solve the equation.
\log(e^{4x})=\log(16)
Take the logarithm of both sides of the equation.
4x\log(e)=\log(16)
The logarithm of a number raised to a power is the power times the logarithm of the number.
4x=\frac{\log(16)}{\log(e)}
Divide both sides by \log(e).
4x=\log_{e}\left(16\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
x=\frac{4\ln(2)}{4}
Divide both sides by 4.
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