SOLUTION: I need help with solving this logarithmic equation log5(x+1)+log5(x-1)=log5 8

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Question 129923: I need help with solving this logarithmic equation
log5(x+1)+log5(x-1)=log5 8
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
log%285%2C%28x%2B1%29%29%2Blog%285%2C%28x-1%29%29=log%285%2C%288%29%29


log%285%2C%28%28x%2B1%29%28x-1%29%29%29=log%285%2C%288%29%29 Combine the logs using the identity log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29




%28x%2B1%29%28x-1%29=8 Now raise both sides as exponents with bases of 5 to eliminate the logs on both sides


x%5E2-1=8 Foil


x%5E2-9=0 Subtract 8 from both sides



%28x%2B3%29%28x-3%29=0 Factor the left side



Now set each factor equal to zero:
x%2B3=0 or x-3=0

x=-3 or x=3 Now solve for x in each case


So the possible answers are
x=-3 or x=3

However, the possible solution x=-3 makes the argument of both logs negative.

So the only solution is x=3