Question

graph the logarithmic function by writing the function in exponential form and making a table of points.
$y = \log_{4}x$
part 1 of 3
$y = \log_{4}x$ written in exponential form is $x = 4^{y}$.
part: 1 / 3
part 2 of 3
make a table of points.

$x$	$y$
$\square$	$-1$
$\square$	$0$
$\square$	$1$
$\square$	$2$

Explanation:

Step1: For \( y = -2 \)

We use the exponential form \( x = 4^y \). Substitute \( y=-2 \) into the equation: \( x = 4^{-2}=\frac{1}{4^2}=\frac{1}{16} \).

Step2: For \( y = -1 \)

Substitute \( y = -1 \) into \( x = 4^y \): \( x=4^{-1}=\frac{1}{4} \).

Step3: For \( y = 0 \)

Substitute \( y = 0 \) into \( x = 4^y \): \( x = 4^0 = 1 \) (since any non - zero number to the power of 0 is 1).

Step4: For \( y = 1 \)

Substitute \( y = 1 \) into \( x = 4^y \): \( x=4^1 = 4 \).

Step5: For \( y = 2 \)

Substitute \( y = 2 \) into \( x = 4^y \): \( x = 4^2=16 \).

Answer:

The table of points is:

\( x \)	\( y \)
\( \frac{1}{4} \)	\( -1 \)
\( 1 \)	\( 0 \)
\( 4 \)	\( 1 \)
\( 16 \)	\( 2 \)