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 3xa. Rewrite the equation in exponential form. x =b. For each given value of y, find the value of x to complete the ordered pair.x = 3Yy(x,y)x = 3-2-2X = 3-1-1x = 300X = 3¹x = 3²12.-2)].0)(0.2)

Answer 1

Step-by-step explanation

We have the equation:

`y=\log_3x.`

a) To express x in terms of y, we take into account the following property of logarithms:

`y=\log_ax\Rightarrow x=a^y.`

Choosing a = 3, we have:

`x=3^y.`

b) Now, we evaluate this function for the values y = -2, -1, 0, 1 and 2. To do that, we simply replace the value of y in the last equation, then we simplify the result:

1) y = -2

Replacing y = -2 in the equation of x, we have:

`x=3^(-2).`

Now, the negative power of a number can be written as the positive power but in the denominator:

`x=(1)/(3^2).`

The 3 square is equal to 3*3 = 9, so we have:

`x=(1)/(9).`

So the point for y = -2 is:

`(x,y)=((1)/(9),-2).`

2) y = -1

3) y = 0

4) y = 1

5) y = 2

`y=2\Rightarrow x=3^2=9\Rightarrow(x,y)=(9,2).`Answer

a) The exponential form is: x = 3^y

b) The values of x for the table are:

• y = -2 ⇒ (,1/9,, -2)

,

• y = -1 ⇒ (,1/3,, -1)

,

• y = 0 ⇒ (,1,, 0)

,

• y = 1 ⇒ (,3,, 1)

• y = 2 ⇒ (,9,, 2)