# Thread: Log q.

1. ## Log q.

Can someone post the solution for this please?
Thanks!

2. Originally Posted by Detanon

Can someone post the solution for this please?
Thanks!
You need to consider the addition of logs law which is

$\log_ab+\log_ac= \log_a(b\times c)$

In your equation

$\log_a\sqrt{x^2-1}+\frac{1}{2}\log_a\left(\frac{x+1}{x-1}\right)$

$\log_a\sqrt{x^2-1}+\log_a\left(\frac{x+1}{x-1}\right)^{\frac{1}{2}}$

now applying the rule you get

$\log_a\left(\sqrt{x^2-1}\times \left(\frac{x+1}{x-1}\right)^{\frac{1}{2}}\right)$

Now finish it by simplifying.