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

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(22740) (Show Source): You can put this solution on YOUR website!
Assume the problem is:
=
:
Use the nat logs
=
:
use the log equiv of exponents
=
:
we know the ln of e = 1, and ln(e^4) = 4, therefore it is greatly simplified
=
-x = 4(x+3)
-x = 4x + 12
-12 = 4x + x
-12 = 5x
x =
:
:
Check this on your calc
enter e^(-(-12/5)) = 11.023
enter (e^4)^((-12/5)+3)= 11.023, equality reigns

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