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.