# Find the inverse function if: 9^x =2e^(x^2)

Find the inverse function if:
${9}^{x}=2{e}^{{x}^{2}}$
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umgangistbf
${9}^{x}=2{e}^{{x}^{2}}$
$9x=2{e}^{{x}^{2}}$
$\mathrm{ln}\left(9x\right)=\mathrm{ln}\left(2{e}^{{x}^{2}}\right)$
$x\left(\mathrm{ln}\left(9\right)\right)=\mathrm{ln}\left(2\right)+\mathrm{ln}\left({e}^{{x}^{2}}\right)$
$x\left(\mathrm{ln}\left(9\right)\right)=\mathrm{ln}\left(2\right)+{x}^{2}$
${x}^{2}-\mathrm{ln}\left(9\right)x+\mathrm{ln}\left(2\right)=0$
now solve using quadratic formula you get
$x=\frac{\mathrm{ln}\left(9\right)+\sqrt{\left[\left(\mathrm{ln}9{\right)}^{2}-4\left(1\right)\left(\mathrm{ln}\left(2\right)\right)\right]}}{2}$