Log7(x)+log7(x-2) = log7(24)

please help me solve this.

For example, let log7(A) = a and log7(B) = b
AB = 7^a * 7^b = 7^(a+b)
log7(AB) = a + b = log7(A) + log7(B)

Let A = x, B = x-2, AB = 24 and you'll have a quadratic equation
x(x-2) = 24
x^2 - 2x - 24 = 0
x = -4, 6

However, since the log function does not apply to negative numbers, x = 6.

multiply the terms in the parenthesis

= log7((x)(x-2)) = log7(24)

therefore...

x(x-2) must equal 24

x^2 - 2x - 24 = 0
(x-6)(x-4) = 0

x= 6,4

good luck!