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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)

A Rewrite The Equation In Exponential Formb Create A Table Of Coordinates Using The Exponential Form From Part A Begin By Selecting 2 1 0 1 And 2 For Yc Using T class=

Sagot :

Explanation

We have the equation:

[tex]y=\log_3x.[/tex]

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

[tex]y=\log_ax\Rightarrow x=a^y.[/tex]

Choosing a = 3, we have:

[tex]x=3^y.[/tex]

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:

[tex]x=3^{-2}.[/tex]

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

[tex]x=\frac{1}{3^2}.[/tex]

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

[tex]x=\frac{1}{9}.[/tex]

So the point for y = -2 is:

[tex](x,y)=(\frac{1}{9},-2).[/tex]

2) y = -1

[tex]y=-1\operatorname{\Rightarrow}x=3^{-1}=\frac{1}{3^1}=\frac{1}{3}\Rightarrow(x,y)=(\frac{1}{3},-1).[/tex]

3) y = 0

[tex]y=0\operatorname{\Rightarrow}x=3^0=1\Rightarrow(x,y)=(1,0).[/tex]

4) y = 1

[tex]y=1\operatorname{\Rightarrow}x=3^1=3\Rightarrow(x,y)=(3,1).[/tex]

5) y = 2

[tex]y=2\Rightarrow x=3^2=9\Rightarrow(x,y)=(9,2).[/tex]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)

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