SOLUTION: Solve, expressing answer in exact form. [(e^x)^3 * (e^x)^2x] / e^5 = 1

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Question 61475: Solve, expressing answer in exact form.
[(e^x)^3 * (e^x)^2x] / e^5 = 1
Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
Solve, expressing answer in exact form.
%28%28e%5Ex%29%5E3+%2A+%28e%5Ex%29%5E%282x%29%29+%2F+e%5E5+=+1
%28e%5Ex%29%5E3+=+e%5E%283x%29
%28e%5Ex%29%5E%282x%29+=+e%5E%282x%5E2%29
So, the original equation becomes: e%5E%283x%29+%2A+e%5E%282x%5E2%29+=+e%5E5.
This is also: e%5E%282x%5E2%2B3x%29+=+e%5E5
So, 2x%5E2%2B3x=5
Or, 2x%5E2%2B3x-5=0.
This factors into %282x%2B5%29%28x-1%29.
So, x=1 and x=-5%2F2 are solutions.