Solve for x
x=\frac{\log_{3}\left(7\right)}{2}\approx 0.885621875
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3^{2x}=7
Swap sides so that all variable terms are on the left hand side.
\log(3^{2x})=\log(7)
Take the logarithm of both sides of the equation.
2x\log(3)=\log(7)
The logarithm of a number raised to a power is the power times the logarithm of the number.
2x=\frac{\log(7)}{\log(3)}
Divide both sides by \log(3).
2x=\log_{3}\left(7\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
x=\frac{\log_{3}\left(7\right)}{2}
Divide both sides by 2.
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