# Find the inverse function if: 2e^(3x)=4e^(5x)

Find the inverse function if:
$2{e}^{3x}=4{e}^{5x}$
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Emilie Reeves
$2{e}^{3x}=4{e}^{5x}$
$2{e}^{3x}=4{e}^{5x}$
${e}^{3x}=2{e}^{5x}$
$\mathrm{ln}\left({e}^{3x}\right)=\mathrm{ln}\left(2{e}^{5x}\right)$
$3x=\mathrm{ln}\left(2\right)+\mathrm{ln}\left({e}^{5x}\right)$
$3x=\mathrm{ln}\left(2\right)+5x$
$-2x=\mathrm{ln}\left(2\right)$
$x-=-\mathrm{ln}\left(2\right)/2$