A value of x that satisfies the equation log(x) + log(x - 7) = log(8) + log(11) is

A. 1
B. 2
C. 7
D. 11

Question

A value of x that satisfies the equation log(x) + log(x - 7) = log(8) + log(11) is

A. 1
B. 2
C. 7
D. 11

Accepted Answer

x = 11 By the product rule, the left side becomes log(x(x-7)) and the right side becomes log(88). Equating arguments gives x(x-7) = 88, or x^2 - 7x - 88 = 0. Factoring yields (x - 11)(x + 8) = 0, so x = 11 or x = -8. Since the argument of a logarithm must be positive and x > 7 is required, only x = 11 is valid.

A value of x that satisfies the equation log(x) + log(x - 7) = log(8) + log(11) is A. 1 B. 2 C. 7 D. 11