SOLUTION: If log(x³+3) - log(x+7) + log2 = logx,find the value of x where the bases are 10.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If log(x³+3) - log(x+7) + log2 = logx,find the value of x where the bases are 10.      Log On


   

Question 1124557: If log(x³+3) - log(x+7) + log2 = logx,find the value of x where the bases are 10.
Found 2 solutions by Alan3354, math_helper:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If log(x³+3) - log(x+7) + log2 = logx,find the value of x where the bases are 10.If log(x³+3) - log(x+7) + log2 = logx,find the value of x where the bases are 10.
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log%282%28x%5E3%2B3%29%2F%28x%2B7%29%29+=+log%28x%29
2%28x%5E3%2B3%29%2F%28x%2B7%29+=+x
2x%5E3%2B6+=+x%5E2%2B7x
2x%5E3+-+x%5E2+-+7x+%2B+6+=+0
x = 1
x = -2 ---- not allowed
You can find the 3rd root.
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PS The base is not relevant.

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28%28x%5E3%2B3%29%29+-+log%28%28x%2B7%29%29+%2B+log%28%282%29%29+=+log%28%28x%29%29+
+log%28%28x%5E3%2B3%29%29+-+log%28%28x%2B7%29%29+=+log%28%28x%29%29+-+log%28%282%29%29++
+log%28%28%28x%5E3%2B3%29%2F%28x%2B7%29%29%29+=+log%28%28x%2F2%29%29++
Raise 10 to each side:
++%28x%5E3%2B3%29%2F%28x%2B7%29+=+%28x%2F2%29+
After some Algebra:
+++2x%5E3-x%5E2-7x%2B6+=+0+
This factors to:
++%282x-3%29%2A%28x-1%29%2A%28x%2B2%29+=+0+
Solutions +highlight%28x=3%2F2%29+ and +highlight%28x=1%29+ work. Discard x = -2 because log(x) not defined for x<0.