Question

a. Rewrite the equation in exponential form.b. Create a table of coordinates, using the exponential form from part (a). Begin by selecting -2, -1, 0, 1, and 2 for y.c. Using the coordinates from part (b), graph the logarithmic function.y = log 4xb. For each given value of y, find the value of x to complete the ordered pair.x = 4yy(x,y)X = 4-2-2(-2)X =4-1-1x = 4⁰0(0.⁰)x = 4¹X = 4²(2)12

Answer 1

Gven

The lograthmic function, lograthmic fu

`y=\log_4x`

To find:

a) Rewrite the function in exponential form.

b) For each given value of y, find the value of x to complete the ordered pair.

c) The graph of the function.

Step-by-step explanation:

It is given that,

`y=\log_4x`

a) Since,

It is known that,

`\begin{gathered} y=\log_ax \\ \Rightarrow x=a^y \end{gathered}`

Then,

`x=4^y`

Hence, the exponential form of the function is,

`x=4^y`

b) Also,

For y = -2,.

The value of x is given by,

`\begin{gathered} \\ \Rightarrow x=4^(-2) \\ \Rightarrow x=(1)/(4^2) \\ \Rightarrow x=(1)/(16) \end{gathered}`

Hence, the ordered pair is (1/16, -2).

For y = -1,

`\begin{gathered} x=4^(-1) \\ x=(1)/(4) \end{gathered}`

Hence, the ordered pair is (1/4, -1).

For y = 0,

`\begin{gathered} x=4^0 \\ x=1 \end{gathered}`

Hence, the ordered pair is (1, 0).

For y = 1,

`\begin{gathered} x=4^1 \\ x=4 \end{gathered}`

Hence, the ordered pair is (4, 1).

For y = 2,

`\begin{gathered} x=4^2 \\ x=16 \end{gathered}`

Hence, the ordered pair is (16, 2).

c) Also, the graph of the given function is,