Log (x-1) - log5=log (x+1) - logx

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