Question 61475
Solve, expressing answer in exact form.
{{{((e^x)^3 * (e^x)^(2x)) / e^5 = 1}}}

{{{(e^x)^3 = e^(3x)}}}
{{{(e^x)^(2x) = e^(2x^2)}}}

So, the original equation becomes: {{{e^(3x) * e^(2x^2) = e^5}}}.
This is also: {{{e^(2x^2+3x) = e^5}}}
So, {{{2x^2+3x=5}}}
Or, {{{2x^2+3x-5=0}}}.
This factors into {{{(2x+5)(x-1)}}}.
So, {{{x=1}}} and {{{x=-5/2}}} are solutions.