How do you simplify #ln (1/e^3)#?

1 Answer
Bill K.
Dec 3, 2015

#ln(1/e^(3))=ln(e^(-3))=-3#.

Explanation:

Since #ln(x)# and #e^{x}# are inverse functions, #ln(e^{x})=x# for all values of #x#.

Since #1/e^{3}=e^{-3}# by definition of negative exponents, it follows that #ln(1/e^(3))=ln(e^(-3))=-3#.

You could also note that #ln(1/e^{3})=ln(1)-ln(e^{3})=0-3=-3# since #ln(A/B)=ln(A)-ln(B)# and #ln(1)=0#.

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