Question

plzzz solve it fast no. vii in the following image through logarithm

solve it by showing all the steps

Answer 1

log{ ( x -2)(x +3) base 6 } = 1

(x -2)(x +3) = 6¹ = 6

x² + x - 6 = 6

x² + x -12 = 0

x² + 4x -3x -12 = 0

x(x +4) -3(x +4) = 0

(x -3) (x +4) = 0

x = 3 , -4

now for log to be defined ,
(x -2)(x +3) > 0

x > 2 or x < -3

so, x = 3 and -4 both are solutions .