SOLUTION: log(x^2+9)-log(x+3)=2+log(x-3) Help please!

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Question 373138: log(x^2+9)-log(x+3)=2+log(x-3)
Help please!
Found 2 solutions by Edwin McCravy, CharlesG2:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28x%5E2%2B9%29%29-log%28%28x%2B3%29%29=2%2Blog%28%28x-3%29%29

log%28%28x%5E2%2B9%29%29-log%28%28x%2B3%29%29-log%28%28x-3%29%29=2

log%28%28x%5E2%2B9%29%29-%28log%28%28x%2B3%29%29%2Blog%28%28x-3%29%29%29=2

log%28%28x%5E2%2B9%29%29-log%28%28%28x%2B3%29%28x-3%29%29%29=2

log%28%28x%5E2%2B9%29%29-log%28%28x%5E2-9%29%29=2

log%28%28%28x%5E2%2B9%29%2F%28x%5E2-9%29%29%29=2

%28%28x%5E2%2B9%29%2F%28x%5E2-9%29%29=10%5E2

%28%28x%5E2%2B9%29%2F%28x%5E2-9%29%29=100

x%5E2%2B9=100%28x%5E2-9%29

x%5E2%2B9=100x%5E2-900

909=99x%5E2

909%2F99=x%5E2

101%2F11=x%5E2

%22%22%2B-+sqrt%28101%2F11%29=x

%22%22%2B-+sqrt%28expr%28101%2F11%29expr%2811%2F11%29%29=x

%22%22%2B-+sqrt%28expr%281111%2F11%5E2%29%29=x

%22%22%2B-+sqrt%28expr%281111%29%29%2F11=x

%22%22%2B-+sqrt%28expr%281111%29%29%2F11=x

%22%22%2B-+3.030151511=x

We discard the negative answer since when substituted
for x in the original requires the logarithm of a negative
number, which is not defined in real numbers.

Answer = sqrt%28expr%281111%29%29%2F11

Edwin

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
log(x^2+9)-log(x+3)=2+log(x-3)
Help please!

log(x^2 + 9) - log(x + 3) = 2 + log(x - 3)
logarithmic rule: logb(m) - logb(n) = logb(m/n)
logarithmic rule: logb(m) + logb(n) = logb(mn)
2 = log 100
log((x^2 + 9)/(x + 3)) = log 100 + log(x - 3)
log((x^2 + 9)/(x + 3)) = log 100(x - 3)
log((x^2 + 9)/(x + 3)) = log 100(x - 3)
(x^2 + 9)/(x + 3) = 100(x - 3) (what is in parenthesis must equal)
x^2 + 9 = 100(x - 3)(x + 3)
x^2 + 9 = 100(x^2 - 9)
x^2 + 9 = 100x^2 - 900
-99x^2 = -909
99x^2 = 909
x^2 = 909/99 = 101/11
x = +- sqrt(101/11)
can not take log of a negative number, so x = -sqrt(101/11) does not work
so x = sqrt(101/11)