Solve for m
m=2\log_{14}\left(3\right)-7\approx -6.167420672
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14^{m+7}=9
Use the rules of exponents and logarithms to solve the equation.
\log(14^{m+7})=\log(9)
Take the logarithm of both sides of the equation.
\left(m+7\right)\log(14)=\log(9)
The logarithm of a number raised to a power is the power times the logarithm of the number.
m+7=\frac{\log(9)}{\log(14)}
Divide both sides by \log(14).
m+7=\log_{14}\left(9\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
m=2\log_{14}\left(3\right)-7
Subtract 7 from both sides of the equation.
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