SOLUTION: Simplify: {{{log( 7, 5x) - log( 7, x+3) = 4log( 7, 3)}}}

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Question 22212: Simplify:
log%28+7%2C+5x%29+-+log%28+7%2C+x%2B3%29+=+4log%28+7%2C+3%29
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
log%287%2C%285x%29%29+-+log%287%2C%28x%2B3%29%29+=+4log%287%2C%283%29%29 Apply the Quotient rule for logarithms: log%28b%2CM%29-log%28b%2CN%29+=+log%28b%2C%28M%2FN%29%29 to the left side. The right side is rewritten because: log%28b%2CM%5Ep%29+=+p%2Alog%28b%2CM%29
log%287%2C%285x%2F%28x%2B3%29%29%29+=+log%287%2C%283%5E4%29%29 If log%28b%2CM%29+=+log%28b%2CN%29 then M=N, so:
5x%2F%28x%2B3%29+=+3%5E4
5x%2F%28x%2B3%29+=+81 Multiply both sides by (x+3)
5x+=+81x+%2B+243 Subtract 243 from both sides.
5x-243+=+81x Subtract 5x from both sides.
-243+=+76x Divide both sides by 76.
x+=+-3.197368