Solve for k
k=3
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5^{k-3}=1
Use the rules of exponents and logarithms to solve the equation.
\log(5^{k-3})=\log(1)
Take the logarithm of both sides of the equation.
\left(k-3\right)\log(5)=\log(1)
The logarithm of a number raised to a power is the power times the logarithm of the number.
k-3=\frac{\log(1)}{\log(5)}
Divide both sides by \log(5).
k-3=\log_{5}\left(1\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
k=-\left(-3\right)
Add 3 to both sides of the equation.
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