SOLUTION: write the following expression as a single logarithm and state restrictions. 4log(x-1)+2log(x+5)-log(x-2)

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Question 252722: write the following expression as a single logarithm and state restrictions. 4log(x-1)+2log(x+5)-log(x-2)
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Let's look at restrictions first:
X can't = 1, 2, or -5
If X equals any of these the log wouldn't exist at log(0).
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step #1 - place all front numbers in exponents (power rule)
%28log%28x-1%29%5E4%29+%2B+%28log%28x%2B5%29%5E2%29+-+log%28x-2%29
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step #2 - add of logs means multiply information and subtract means divide information. SO,
log%28%28x-1%29%5E4%2A%28x%2B5%29%5E2%29%2F%28x-2%29
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step #3 - simplify the numerator. This is not the fun step . . .
log%28x%5E6%2B6x%5E5-9x%5E4-44x%5E3%2B111x%5E2-90x%2B25%29%2F%28x-2%29