SOLUTION: solve the exponential equation. Two decimal places for solution e^2x+e^x-6=0 The 2x and x on the e are above. Can you help me answer this one?

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Question 197337This question is from textbook
: solve the exponential equation. Two decimal places for solution
e^2x+e^x-6=0
The 2x and x on the e are above. Can you help me answer this one? This question is from textbook

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
e%5E2x%2Be%5Ex-6+=+0 Treat the e as a variable and factor the trinomial.
%28e%5Ex-2%29%28e%5Ex%2B3%29+=+0 Apply the zero product rule.
e%5Ex-2+=+0 or e%5Ex%2B3+=+0 so...
e%5Ex+=+2 or e%5Ex+=+-3 Take the natural log of both sides of these two results.
ln%28e%5Ex%29+=+ln%282%29 or ln%28e%5Ex%29+=+ln%28-3%29 Apply the power rule for logarithms.
x%2Aln%28e%29+=+ln%282%29 or x%2Aln%28e%29+=+ln%28-3%29 Evaluate.
highlight%28x+=+0.693%29 or highlight%28x+=+1.098%2B3.14i%29