log9 x + log9 (x-8) =1

log₉ x + log₉ (x-8) =1   using  a couple of log properties, we have

log₉ [ (x)(x - 8) ]  = log₉ 9    so we have

(x)(x - 8) = 9  simplify

x^2 - 8x - 9 = 0  factoor

(x - 9) (x + 1)  = 0      and setting each factor to 0, we have x = 9 and x = -1   ..  reject the negative answer..

So x = 9