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

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) (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)

Since log A = log B means that A=B, in the same way
means that

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) (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

RELATED QUESTIONS
write as a single log: 1/2log (x)-1/2log(y)-1/3 log(z) (answered by stanbon)
2log(x+2)=log3+log(2x+1) (answered by nerdybill)
Simplify (a) 2log(5x)-log((x^3)�4)+logx (b) log... (answered by josgarithmetic)
How to solve 2log(x+1) - log (x+3) =... (answered by Theo)
log x + log(x+1)=2 what does x equal? (answered by MathLover1)
log in base 3(2x+1)=2 what does x... (answered by dabanfield)
solve 2log X- log(X-2) =2 log... (answered by ikleyn)
log(4)x=2log(4)3 (answered by jsmallt9)
2log(x)-log(10)-3=0 (answered by mananth)