log8((x^2)-16)-log8(x-4) using laws of logrythm

The following works for all bases, including base 8:

log(x² - 16) - log(x - 4)

Since logs are subtracted when the problem is a division problem:

=  log( (x² - 16) / (x - 4) )

=  log( (x - 4)(x + 4) / (x - 4) )

=  log( x + 4)