Question

A student was asked to determine the y-intercept for the logarithmic function f (x) = log2(x + 3) + 1. Which of the following expressions would result in the correct y-intercept? A. log2/log3 +1 B. log3/log2+1 C. 2–1 – 3 D. (–1)2 – 2

Answer 1

To find the y-intercept we going to set x=0

$\begin{gathered} f(x)=\log_2\left(x+3\right)+1 \\ f(x)=\operatorname{\log}_2(0+3)+1 \\ f(x)=\operatorname{\log}_2(3)+1 \end{gathered}$

But we don't have exactly that value on the answer

So we need to apply logarithm properties, in this case, base change

$\log_ba=\frac{\log_ca}{\operatorname{\log}_cb}$

Appling to our problem

$f(x)=\frac{\operatorname{\log}3}{\operatorname{\log}2}+1$

Answer: Option B log3/log2+1