1. ## Natural logarithm equation

Hello,

How do I solve the following equation? $\displaystyle \ln{(x-5)}+\ln{(x+16)} = \ln{(5)}$

I tried the following, but apparently this is not correct, i.e. score = 0%.

$\displaystyle \ln{(x-5)}+\ln{(x+16)} = \ln{(5)}$
$\displaystyle \ln{((x-5)(x+16))} = \ln{(5)}$
$\displaystyle (x-5)(x+16) = 5$
$\displaystyle x^2+16x-5x-80 = 5$
$\displaystyle x^2+11x-85 = 0$
$\displaystyle D = b^2-4ac = 11^2-4*1*-85 = 121 - (-340) = 121+340 = 461$
$\displaystyle x_1 = \frac{-b+\sqrt{D}}{2a} = \frac{-11+\sqrt{461}}{2}$
$\displaystyle x_2 = \frac{-b-\sqrt{D}}{2a} = \frac{-11-\sqrt{461}}{2}$

2. ## Re: Natural logarithm equation

What's the domain of log?

3. ## Re: Natural logarithm equation

Originally Posted by JakeBarnes
What's the domain of log?
I know $\displaystyle \ln{(x)}$ is only defined for $\displaystyle x > 0$. So one of the answers should be correct, but the problem is none of them are...

4. ## Re: Natural logarithm equation

As we have ln(x-5) in the equation any solution must be >5
I know $\displaystyle \ln{(x)}$ is only defined for $\displaystyle x > 0$. So one of the answers should be correct, but the problem is none of them are...