Solve for x
x=\frac{1-2\ln(2)}{3}\approx -0.128764787
Solve for x (complex solution)
x=-\frac{i\times 2\pi n_{1}}{3}-\frac{2\ln(2)}{3}+\frac{1}{3}
n_{1}\in \mathrm{Z}
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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.
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