Solve for b
b=\frac{\log_{5}\left(106\right)}{3}\approx 0.965852541
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5^{3b}=106
Use the rules of exponents and logarithms to solve the equation.
\log(5^{3b})=\log(106)
Take the logarithm of both sides of the equation.
3b\log(5)=\log(106)
The logarithm of a number raised to a power is the power times the logarithm of the number.
3b=\frac{\log(106)}{\log(5)}
Divide both sides by \log(5).
3b=\log_{5}\left(106\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
b=\frac{\log_{5}\left(106\right)}{3}
Divide both sides by 3.
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