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 where the function crosses the $x$-axis, which means that the value of $y$ is equal to 0. So we need to solve the equation:
$$0 = 3 + \log _{4} x$$
Subtracting 3 from both sides, we get:
$$-3 = \log _{4} x$$
Using the definition of logarithms, we can rewrite this as:
$$4^{-3} = x$$
Simplifying, we get:
$$x = \frac{1}{64}$$
So the answer is B.

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