Question

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

Answer 1

`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`