Solve for a
a=\ln(3)\approx 1.098612289
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e^{2a}=9
Use the rules of exponents and logarithms to solve the equation.
\log(e^{2a})=\log(9)
Take the logarithm of both sides of the equation.
2a\log(e)=\log(9)
The logarithm of a number raised to a power is the power times the logarithm of the number.
2a=\frac{\log(9)}{\log(e)}
Divide both sides by \log(e).
2a=\log_{e}\left(9\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
a=\frac{2\ln(3)}{2}
Divide both sides by 2.
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