Solve for x
x=2
Solve for x (complex solution)
x=\frac{i\pi n_{1}}{3\ln(5)}+2
n_{1}\in \mathrm{Z}
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5^{6x-9}=125
Use the rules of exponents and logarithms to solve the equation.
\log(5^{6x-9})=\log(125)
Take the logarithm of both sides of the equation.
\left(6x-9\right)\log(5)=\log(125)
The logarithm of a number raised to a power is the power times the logarithm of the number.
6x-9=\frac{\log(125)}{\log(5)}
Divide both sides by \log(5).
6x-9=\log_{5}\left(125\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
6x=3-\left(-9\right)
Add 9 to both sides of the equation.
x=\frac{12}{6}
Divide both sides by 6.
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Limits
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