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

Question 129923: I need help with solving this logarithmic equation
log5(x+1)+log5(x-1)=log5 8
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Combine the logs using the identity

Now raise both sides as exponents with bases of 5 to eliminate the logs on both sides

Foil

Subtract 8 from both sides

Factor the left side

Now set each factor equal to zero:
or

or Now solve for x in each case

So the possible answers are
or

However, the possible solution makes the argument of both logs negative.

So the only solution is
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