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5^{4x}=415
Use the rules of exponents and logarithms to solve the equation.
\log(5^{4x})=\log(415)
Take the logarithm of both sides of the equation.
4x\log(5)=\log(415)
The logarithm of a number raised to a power is the power times the logarithm of the number.
4x=\frac{\log(415)}{\log(5)}
Divide both sides by \log(5).
4x=\log_{5}\left(415\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
x=\frac{\log_{5}\left(415\right)}{4}
Divide both sides by 4.