I had a problem similar to this one.
Write expression as a logarithm of a single quantity and then simplify if possible.
(1/4)[log (x²-1)-log (x+1)]+3log x
Please show the steps.
Hello,
Note that x>0 and |x|>1, so x>1. Otherwise it is not defined.
notice that x²-1=(x-1)(x+1)
So $\displaystyle \log(x^2-1)-\log(x+1)=\log \left(\frac{x^2-1}{x+1}\right)=\log(x-1)$
$\displaystyle \frac 14 \cdot \log(x-1)+3 \log(x)=\log \left((x-1)^{1/4}\right)+\log(x^3)$
$\displaystyle =\log \left((x-1)^{1/4} \cdot x^3\right)=\log \left((x^{13}-x^{12})^{1/4}\right)$
now it depends on how you want it to be simplified.