Solve the logarithmic equation Be sure to reject any value t

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. log_9 (x^2 - 8x) =1 A) {1} B) {-9, 1} C) {9, -1} D) {9}

Solution

Solution:

log₉(x^2-8x) =1

log₉(x^2-8x) = log₉9¹

(x^2-8x) = 9

(x-9) (x+1) = 0

x = 9 and x = -1

x = -1 will be neglected because it is not in the domain of log(x^2-8x)

therefore x = 9 is the answer

option D : [9] is correct