Graph $y = \log _ { \frac { 1 } { 4 } } x$ by graphing $\left( \frac { 1 } { 4 } \right) ^ { y } = x$ .

Question

Quizplus · Accepted Answer

To graph $y = \log _ { \frac { 1 } { 4 } } x$, we need to rewrite it in exponential form:

$$x=\left(\frac{1}{4}\right)^y$$

Now, we can create a table of values by choosing some values for $y$ and calculating the corresponding values for $x$:

\begin{array}{|c|c|}
\hline
y & x \ \hline
-2 & 16 \ 
-1 & 4 \ 
0 & 1 \ 
1 & \frac{1}{4} \ 
2 & \frac{1}{16}\ 
\hline
\end{array}

Using these points, we can plot the graph:

graph{log(1/4, x)}

Alternatively, we can notice that the equation $\left( \frac { 1 } { 4 } \right) ^ { y } = x$ is the same as $y=\log_{\frac{1}{4}}x$, since $\log_a b=c$ is equivalent to $a^c=b$. Therefore, graphing $\left( \frac { 1 } { 4 } \right) ^ { y } = x$ gives us the same graph as $y=\log_{\frac{1}{4}}x$.

Either way, the correct answer is choice B.

Graph y=log⁡14xy = \log _ { \frac { 1 } { 4 } } xy=log41​​x

Graph $y = \log _ { \frac { 1 } { 4 } } x$