Identify the $x$-intercept of the function $y = 3 + \log _ { 4 } x$.
A) 64
B) $\frac { 1 } { 64 }$
C) $- 3$
D) 12
E) The function has no $x$-intercept.

Question

Quizplus · Accepted Answer

To find the $x$-intercept, we need to find the value of $x$ when $y=0$. So we set $y$ to zero and solve for $x$:
$$0=3+\log_4x$$
$$\Rightarrow -3=\log_4x$$
$$\Rightarrow 4^{-3}=x$$
$$\Rightarrow \frac{1}{64}=x$$
Therefore, the $x$-intercept of the function is $\frac{1}{64}$, so the answer is choice B.

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