SOLUTION: I have two similiar problems to solve. If I can get help with how to solve one of them, I'm sure I can work the other. e^(x-8) = 33 3^(4x-3) = 3

Question 83637: I have two similiar problems to solve. If I can get help with how to solve one of them, I'm sure I can work the other.
e^(x-8) = 33
3^(4x-3) = 3

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
e^(x-8) = 33
:
Using nat logs:
ln(e^(x-8)) = ln(33)
:
Log equiv of exponents:
(x-8)*ln(e) = ln(33)
:
Find the ln of both sides. Nat ln of e = 1, remember
x - 8 = 3.4965
x = 3.4965 + 8
x = 11.4965
:
Check solution on a good calc: enter: e^(11.4965-8); should get 32.99975
:
:
3^(4x-3) = 3
Just looking at it you know that 4x-3 = 1, but here is the method anyway
:
Using nat logs again
ln(3^(4x-3) = ln(3)
:
(4x-3)*ln (3) = ln(3)
(4x-3)*1.0986 = 1.0986
4x - 3 = 1.0986/1.0986
4x - 3 = 1
4x = 1 + 3
4x = 4
x = 4/4
x = 1
:
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