Question

Which of the following is true regarding the solution to the logarithmic equation below?

log Subscript 2 Baseline (x + 11) = 4. x + 11 = 2 Superscript 4. x + 11 = 16. x = 5.
x = 5 is not a true solution because log Subscript 5 Baseline (16) not-equals 2
x = 5 is not a true solution because log Subscript 5 Baseline (16) not-equals 4
x = 5 is a true solution because log Subscript 2 Baseline (16) = 4
x = 5 is a true solution because log Subscript 4 Baseline (16) = 2

Answer 1

"x = 5 is a true solution because log₂(16) = 4."

Reason: log₂(x+11)=4 ⇒ x+11=2⁴=16 ⇒ x=5, and indeed log₂(5+11)=log₂(16)=4. The other choices use the wrong base (log₅) or are irrelevant (log₄(16)=2 is true but not the reason).