Solve for m
m=\frac{3}{8}=0.375
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625^{2m}=125
Use the rules of exponents and logarithms to solve the equation.
\log(625^{2m})=\log(125)
Take the logarithm of both sides of the equation.
2m\log(625)=\log(125)
The logarithm of a number raised to a power is the power times the logarithm of the number.
2m=\frac{\log(125)}{\log(625)}
Divide both sides by \log(625).
2m=\log_{625}\left(125\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
m=\frac{\frac{3}{4}}{2}
Divide both sides by 2.
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