SOLUTION: Solve the following equation by using properties of logarithms: e^(x-1)-5=5 (The x-1 is the entire exponent) Thank you!

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Question 730277: Solve the following equation by using properties of logarithms: e^(x-1)-5=5
(The x-1 is the entire exponent)
Thank you!
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!
. 

Starting equation is

    e%5E%28x-1%29 - 5 = 5


Add 5 to both sides

    e%5E%28x-1%29 = 5 + 5 = 10.


Take natural logarithm of both sides

    (x-1)*ln(e) = ln(10)


Use ln(e) = 1

    x - 1 = ln(10)


ANSWER.  x = ln(10) + 1 = 3.302585093...


CHECK.  e%5E%28x-1%29-5 = 2.7182818284%5E%283.302585093-1%29-5 = 4.9999999996,  which is good match.

Solved.