SOLUTION: If log(x+3) - log(x+1) = 2, then x=

Question 1169433: If log(x+3) - log(x+1) = 2, then x=
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
start with:
log(x+3) - log(x+1) = 2
since log(x+3) - log(x+1) = log((x+3)/(x+1)), the equation becomes:
log((x+3)/(x+1)) = 2
this is true if and only if 10^2 = (x+3)/(x+1)
multiply both sides of this equation by (x+1) to get:
10^2 * (x+1) = x+3
simplify to get:
100 * x + 100 = x + 3
subtract x from both sides of the equation and subtract 100 from both sides of the equation to get:
100*x - x = 3 - 100
combine like terms to get:
99*x = -97
solve for x to get:
x = -97/99

confirm by replacing x with -97/99 in the original equation to get:
log(x+3) - log(x+1) = 2 becomes:
log(-97/99 + 3) - log(-97/99 + 1) = 2
do the math to get:
2 = 2
this confirms the value of x is good.

your solution is that x = -97/99
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