SOLUTION: Solve a)log(base 2)(x+1) + log(base 2)(x-1) = 3 b)log(base 2)(x+2) = 2 - log(base 2)(x-1) Can you please help me out? Thanks so much in advance:)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve a)log(base 2)(x+1) + log(base 2)(x-1) = 3 b)log(base 2)(x+2) = 2 - log(base 2)(x-1) Can you please help me out? Thanks so much in advance:)       Log On


   

Question 867254: Solve
a)log(base 2)(x+1) + log(base 2)(x-1) = 3
b)log(base 2)(x+2) = 2 - log(base 2)(x-1)
Can you please help me out? Thanks so much in advance:)

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve
a)log%282%2C%28x%2B1%29%29+%2B+log%282%2C%28x-1%29%29+=+3
addition of logs, is multiply
log%282%2C%28%28x%2B1%29%28x-1%29%29%29+=+3
FOIL
log%282%2C%28x%5E2-1%29%29+=+3
Write exponent equiv of logs
x^2 -1 = 2%5E3%29
x^2 - 1 = 8
x^2 - 1 - 8 = 0
x^2 - 9 = 0
Factors to
(x-3)(x+3) = 0
x = +3, is the only solution (no negative allowed in a log)
:
b)log%282%2C%28x%2B2%29%29+=+2+-+log%282%2C%28x-1%29%29
log%282%2C%28x%2B2%29%29+%2B+log%282%2C%28x-1%29%29=+2
log%282%2C%28%28x%2B2%29%28x-1%29%29%29+=+2
log%282%2C%28x%5E2%2Bx-2%29%29+=+2
The exponent equiv
x^2 + x - 2 = 2%5E2
x^2 + x - 2 = 4
x^2 + x - 2 - 4 = 0
x^2 + x - 6 = 0
Factors to
(x+3)(x-2) = 0
x = 2, the positive solution all we want here