SOLUTION: 2log(x+3) - log(x+1) = log(2x+3) What does x equal??

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Question 15879: 2log(x+3) - log(x+1) = log(2x+3) What does x equal??
Found 2 solutions by rapaljer, venugopalramana:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Ir may help to rewrite the equation:
2log(x+3) = log(x+1) + log(2x+3)
log%28%28x%2B3%29%29%5E2+=+log+%28%28x%2B1%29%282x%2B3%29%29

Since log A = log B means that A=B, in the same way
log%28%28x%2B3%29%29%5E2+=+log+%28%28x%2B1%29%282x%2B3%29%29 means that %28x%2B3%29%5E2+=+%28x%2B1%29%2A%282x%2B3%29+
x%5E2+%2B+6x+%2B9+=+2x%5E2+%2B5x+%2B+3
0+=+x%5E2-x-6
0+=+%28x-3%29%28x%2B2%29+
x= 3 or x= -2

You must reject x=-2, since it gives you the log of a negative, which is not defined in the resl numbers. The final answer is x=3.

R^2 at SCC

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
2log(x+3) - log(x+1) = log(2x+3)
2log(x+3) - log(x+1) - log(2x+3)=0
using the formula log xy = log x + log y
and log x/y = log x - log y and log x^n = n*log x , we get
log (x+3)^2/[(x+1)*(2x+3)] =0 = log (1)
hence (x+3)^2/[(x+1)*(2x+3)] =1
(x+3)^2 =(x+1)*(2x+3)
x^2+6x+9 = 2x^2+5x+3
2x^2+5x+3 - (x^2+6x+9) = 0
2x^2+5x+3 -x^2-6x-9 = 0
x^2 -x -6 = 0.......find 2 factors of -6 whose sum is -1....namely -3 and 2
x^2 +2x - 3x -6 = 0
x(x+2) - 3 (x+2) = 0
(x-3)(x+2) = 0.........x-3 = 0 ....Or x+2 =0
hence x=3 or -2