Question

Which of the following shows the extraneous solution to the logarithmic equation log Subscript 7 Baseline (3 x cubed + x) minus log Subscript 7 Baseline (x) = 2
x = negative 16
x = negative 4
x = 4
x = 16

Answer 1

Solve: log_7(3x^3 + x) - log_7(x) = log_7((3x^3 + x)/x) = 2, so (3x^3 + x)/x = 49.

This gives 3x^2 + 1 = 49 → 3x^2 = 48 → x^2 = 16 → x = ±4.

But log_7(x) requires x > 0, so x = 4 is valid and x = −4 is extraneous.

Answer: x = negative 4.