SOLUTION: log5(3x+7) + log5(x-5)= 2

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Question 818289: log5(3x+7) + log5(x-5)= 2
Found 2 solutions by LinnW, MathTherapy:
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
log5(3x+7) + log5(x-5)= 2log5(5)
log5(3x+7) + log5(x-5)= log5(5^2)
log5( (3x+7)/(x-5) ) = log5(25)
%283x%2B7%29%2F%28x-5%29++=+25%2F1
%283x%2B7%29++=+25%28x-5%29
3x%2B7++=+25x-125%29
Subtract 3x from each side.
7++=+22x-125%29
Add 125 to each side.
132 = 22x
6 = x

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
log5(3x+7) + log5(x-5)= 2 


log+%285%2C+%283x+%2B+7%29%29+%2B+log+%285%2C+%28x+-+5%29%29=+2

log+%285%2C+%283x+%2B+7%29%28x+-+5%29%29+=+2

%283x+%2B+7%29%28x+-+5%29+=+5%5E2

3x%5E2+-+8x+-+35+=+25

3x%5E2+-+8x+-+60+=+0

(3x + 10){x - 6) = 0

3x = - 10             OR        x = 0 + 6

x+=+-+10%2F3               OR        x+=+6

Since -+10%2F3 will yield the log of a negative number, so ignore this solution. Thus, the only solution is: highlight_green%28x+=+6%29

You can do the check!!



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