What are possible values of x if # lne^(2x)/2<4ln(e^(3x))+5?#?

1 Answer
May 22, 2016

Answer:

#x > -5/11#

Explanation:

#(log_e(e^{2x}))/2=log_e(e^{2x})^{1/2} = log_e(e^x)#
#4 log_e(e^{3x}))=log_e(e^{3x})^4=log_e(e^{12x})#
then
#(log_e(e^{2x}))/2-4 log_e(e^{3x})=log_e((e^x)/(e^{12x})) = log_e(e^{x-12x}) = log_e(e^{-11x})# following
# log_e(e^{-11x}) < log_e(e^5) # and
#log_e(e^{-11x-5})< log_e(1) = 0#
Finally
#e^{-11x-5}<1->-11x-5<0->x > -5/11#