SOLUTION: log_9(x-5)+log_9(x-5)=1

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Question 1078279: log_9(x-5)+log_9(x-5)=1
Answer by ikleyn(52908) About Me  (Show Source):
You can put this solution on YOUR website!
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log%289%2C%28x-5%29%29+%2B+log%289%2C%28x-5%29%29 = 1  --->

log%289%2C%28%28x-5%29%5E2%29%29 = 1  --->

%28x-5%29%5E2 = 9  --->

%28x-5%29%5E2 = 3%5E2  --->

x - 5 = +/- 3  --->


1.  x-5 = 3  --->  x = 8.


2.  x - 5 =  -3  --->  x = -3 + 5 = 2.


Only x = 8 survives under the logarithm.


Answer.  x = 8  is the only solution.