# Solve for x using log50=600e^{-0.4x}

Solve for x using $\mathrm{log}50=600{e}^{-0.4x}$
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Macsen Nixon

To solve equation
$50=600{e}^{-0.4x}$
$\frac{50}{600}={e}^{-0.4x}$
taking ln of both sides we get
$\mathrm{ln}\left(50/600\right)=\mathrm{ln}{e}^{-0.4x}$
$\mathrm{ln}0.08=\mathrm{ln}{e}^{-0.4x}$
since $\mathrm{ln}{e}^{x}=x$
$x=-\frac{\left(-2.53\right)}{0.4}$
$=6.32$
Hence $x=6.32$
Result: $x=6.32$