SOLUTION: Solve for x: ln(7-x)+ln(3x+5)=ln(24x)

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Question 5352: Solve for x:
ln(7-x)+ln(3x+5)=ln(24x)
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Combine logarithms on the left side using the law of logarithms: ln+a+%2B+ln+b+=+ln+%28ab%29+

ln(7-x)+ln(3x+5)=ln(24x)
ln (7-x)(3x+5) = ln(24x)

Raise both sides as a power of e to "undo" the lns:
(7-x)(3x + 5) = 24x
21x+%2B+35+-+3x%5E2+-+5x+-+24x+=+0
-8x+-+3x%5E2+%2B35+=+0

Multiply both sides by -1, and write in descending powers of x:
3x%5E2+%2B+8x+-+35+=+0, which just happens to factor!! (Imagine that!!)
%283x-+7%29%28x%2B5%29+=+0+
x=+7%2F3 x=+-5

You are not allowed to have a log of a negative in the real numbers, so you must reject the -5. The final answer is x=+7%2F3.

R^2 at SCC