SOLUTION: I am having difficulty on the steps to solve this equation: e^-x = (e^4)^x+3 Any help would be greatly appreciated!

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Question 267905: I am having difficulty on the steps to solve this equation:
e^-x = (e^4)^x+3
Any help would be greatly appreciated!
Answer by ankor@dixie-net.com(15622) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the problem is:
e%5E%28-x%29=%28e%5E4%29%5E%28x%2B3%29
:
Use the nat logs
ln%28e%5E%28-x%29%29=ln%28%28e%5E4%29%5E%28x%2B3%29%29
:
use the log equiv of exponents
-x%2Aln%28e%29 = %28x%2B3%29%2Aln%28e%5E4%29
:
we know the ln of e = 1, and ln(e^4) = 4, therefore it is greatly simplified
-x%2A1 = %28x%2B3%29%2A%284%29
-x = 4(x+3)
-x = 4x + 12
-12 = 4x + x
-12 = 5x
x = -12%2F5
:
:
Check this on your calc
enter e^(-(-12/5)) = 11.023
enter (e^4)^((-12/5)+3)= 11.023, equality reigns