Hi, I just don't get this sort of Logarithm problems that have same two variable in the equation.

The problem is:

Solve for x

log x + log(x+3)=1

thanks for the help =]

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- Mar 16th 2008, 06:58 PMcbbplanetbasic logarithm problem
Hi, I just don't get this sort of Logarithm problems that have same two variable in the equation.

The problem is:

Solve for x

log x + log(x+3)=1

thanks for the help =] - Mar 16th 2008, 07:02 PMTheEmptySet
Rewrite using log properties

$\displaystyle Log(x(x+3))=1$

rewrite in expo form.

$\displaystyle x(x+3)=10 \iff x^2+3x-10=0 $

$\displaystyle (x-2)(x+5)=0$

So x=2 or x=-5

But if you plug x=-5 into the original equation you end up with the log(-5)

which is undefined. So the only solution is x=2.