SOLUTION: log (x^2+x-6)^2 to base x+1 = 4

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Question 971464: log (x^2+x-6)^2 to base x+1 = 4
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
log (x^2+x-6)^2 to base x+1 = 4
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log%28%28x%2B1%29%2C%28x%5E2%2Bx-6%29%5E2%29+=+4
--> %28x%2B1%29%5E4+=+%28x%5E2%2Bx-6%29%5E2
%28x%2B1%29%5E2+=+%28x%5E2%2Bx-6%29
x%5E2+%2B+2x+%2B+1%29+=+x%5E2%2Bx-6
2x+1 = x-6
x = -7 --> base -6, not allowed
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%28x%2B1%29%5E2+=+-%28x%5E2%2Bx-6%29
x%5E2+%2B+2x+%2B+1%29+=+-x%5E2+-+x+%2B+6
2x%5E2+%2B+3x+-+5+=+0
(2x + 5)*(x - 1) = 0
x = 1 --> log(-4) not allowed
x = -5/2 --> base -1.5 not allowed