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

For an $x$-intercept, we need $y = 0$. So we set $0 = 3 + \log _ { 4 } x$, and solve:
\begin{align*}
-3 &= \log _ { 4 } x \
4 ^ { -3 } &= x \
\frac{1}{64} &= x
\end{align*}
So the $x$-intercept is $(\frac{1}{64}, 0)$, which corresponds to choice $\boxed{\textbf{(B)}}$.

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