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Solve for x
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Solve for x (complex solution)
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e^{-3x+1}=4
Use the rules of exponents and logarithms to solve the equation.
\log(e^{-3x+1})=\log(4)
Take the logarithm of both sides of the equation.
\left(-3x+1\right)\log(e)=\log(4)
The logarithm of a number raised to a power is the power times the logarithm of the number.
-3x+1=\frac{\log(4)}{\log(e)}
Divide both sides by \log(e).
-3x+1=\log_{e}\left(4\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
-3x=2\ln(2)-1
Subtract 1 from both sides of the equation.
x=\frac{2\ln(2)-1}{-3}
Divide both sides by -3.