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Solve for x
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Solve for x (complex solution)
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18^{9x}+7=46
Use the rules of exponents and logarithms to solve the equation.
18^{9x}=39
Subtract 7 from both sides of the equation.
\log(18^{9x})=\log(39)
Take the logarithm of both sides of the equation.
9x\log(18)=\log(39)
The logarithm of a number raised to a power is the power times the logarithm of the number.
9x=\frac{\log(39)}{\log(18)}
Divide both sides by \log(18).
9x=\log_{18}\left(39\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
x=\frac{\log_{18}\left(39\right)}{9}
Divide both sides by 9.