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

1 Answer
Oct 23, 2015

Answer:

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

Explanation:

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.