Solve for x
x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333
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125^{2x-2}=390625
Use the rules of exponents and logarithms to solve the equation.
\log(125^{2x-2})=\log(390625)
Take the logarithm of both sides of the equation.
\left(2x-2\right)\log(125)=\log(390625)
The logarithm of a number raised to a power is the power times the logarithm of the number.
2x-2=\frac{\log(390625)}{\log(125)}
Divide both sides by \log(125).
2x-2=\log_{125}\left(390625\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
2x=\frac{8}{3}-\left(-2\right)
Add 2 to both sides of the equation.
x=\frac{\frac{14}{3}}{2}
Divide both sides by 2.
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Limits
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