SOLUTION: Solve a) log4(base 4)(x+3) + log4(x-3) = 2 Can you please help me out? Thanks so much in advance:)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve a) log4(base 4)(x+3) + log4(x-3) = 2 Can you please help me out? Thanks so much in advance:)      Log On


   

Question 878678: Solve
a) log4(base 4)(x+3) + log4(x-3) = 2
Can you please help me out? Thanks so much in advance:)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C%28x%2B3%29%29%2Blog%284%2C%28x-3%29%29+=+2


log%284%2C%28%28x%2B3%29%28x-3%29%29%29+=+2


%28x%2B3%29%28x-3%29+=+4%5E2


%28x%2B3%29%28x-3%29+=+16


x%5E2-9+=+16


x%5E2+=+16%2B9


x%5E2+=+25


x+=+%22%22%2B-sqrt%2825%29


x+=+sqrt%2825%29 or x+=+-sqrt%2825%29


x+=+5 or x+=+-5


Those are the possible solutions.
However, only x=5 works because x+=+-5 is NOT in the domain of log%284%2C%28x-3%29%29.
Remember the domain of log%28b%2C%28x%29%29 is x%3E0 (so the domain of log%284%2C%28x-3%29%29 is x%3E3)


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The only solution is x=5