SOLUTION: Solve for x: e^(x)+e^(2x)=12

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Question 934515: Solve for x:
e^(x)+e^(2x)=12
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
e^(x)+e^(2x)=12
==============
Solve for x:
e^(2x) + e^x - 12 = 0
(e^x + 4)*(e^x - 3) = 0
---
e^x = -4 (Ignore)
e^x = 3
x = ln(3)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
e%5Ex%2Be%5E%282x%29=12
e%5Ex%2Be%5Ex%2Ae%5Ex=12
e%5Ex%2A%28e%5Ex%2B1%29+=3%2A4
if product same then corresponding factors are same too; so, we have
e%5Ex=+3
and
e%5Ex%2B1+=+4=>e%5Ex+=+4-1=>e%5Ex=+3
log%28e%5Ex%29=+log%283%29
x%2Alog%28e%29=+log%283%29......log%28e%29=1
x+=+log%283%29