How do you solve for x?: $e^(-2x) = 1/3?$

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Answer 1 · 2015-10-23T16:29:50

$x=ln(3)/2~~0.54930614433$

Convert the equation to logarithm form.

$color(white)(XX)e^(-2x)=1/3$

$color(white)(XX)hArrlog_e(1/3)=-2x$

$color(white)(XX)ln(1/3)=-2x$

Isolate x.

$color(white)(XX)(-1/2)[ln(1/3)]=(-1/2)(-2x)$

$color(white)(XX)(-ln(1/3))/2=x$

Simplify.

$color(white)(XX)ln((1/3)^-1)/2=x$ Theorem: Logarithm of a Power

$color(white)(XX)color(red)(x=ln(3)/2)$

You can leave the answer at that since you can't really get $ln(3)$ without a calculator. The actual answer is around 0.54930614433.

How do you solve for x?: e^(-2x) = 1/3?e^(-2x) = 1/3?