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Solve for x
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Solve for x (complex solution)
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5e^{x}+2=8
Use the rules of exponents and logarithms to solve the equation.
5e^{x}=6
Subtract 2 from both sides of the equation.
e^{x}=\frac{6}{5}
Divide both sides by 5.
\log(e^{x})=\log(\frac{6}{5})
Take the logarithm of both sides of the equation.
x\log(e)=\log(\frac{6}{5})
The logarithm of a number raised to a power is the power times the logarithm of the number.
x=\frac{\log(\frac{6}{5})}{\log(e)}
Divide both sides by \log(e).
x=\log_{e}\left(\frac{6}{5}\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).