Re write it in so that to have one single entity on the left & same on the right
log(x-1)-log5 = log[(x-1)/5]
and log(x+1)-logx = log[(x+1)/x]
So:
log[(x-1)/5] = log[(x+1)/x] ==> (x-1)/5 = (x+1)/x
Now you can solve it: x(x-1)=5(x+1)
==> x² - 6x -5 =0
Solving this quadratic equation gives x'=3+√14 & x" =3-√14
