Question

Which of the following shows the extraneous solution to the logarithmic equation below?

2 log Subscript 5 Baseline (x + 1) = 2
x = negative 6
x = negative 4
x = negative 2
x = negative 1

Answer 1

Answer: x = -6.

Reason: 2 log_5(x+1)=2 ⇒ log_5(x+1)=1 ⇒ x+1=5 ⇒ x=4. If you instead exponentiate: (x+1)^2=25 ⇒ x=4 or x=-6, but x=-6 is invalid because x+1 must be >0 for the log. Thus -6 is extraneous.