I am having trouble with this one… Can someone please show me the steps, the pairs to plot and the asymptotic?

Thank you in advance!

Evaluate the logarithmic equation for three values of x that are greater than 2, three values of x that are between 1 and 2, and at x=2. Show your work. Use the resulting ordered pairs to plot the graph. State the equation of the line asymptotic to the graph (if any).

y = log3 (x - 1)

To evaluate the logarithmic equation y = log3(x - 1), you need to substitute different values of x and solve for y. Here are the steps to evaluate the equation for the given values and plot the graph:

1. Choose three values of x that are greater than 2:
Let's say we choose x = 3, 4, and 5.

For x = 3:
y = log3(3 - 1) = log3(2)
Calculate the logarithm base 3 of 2 to find the corresponding value of y for this x.

For x = 4:
y = log3(4 - 1) = log3(3)
Calculate the logarithm base 3 of 3 to find the corresponding value of y for this x.

For x = 5:
y = log3(5 - 1) = log3(4)
Calculate the logarithm base 3 of 4 to find the corresponding value of y for this x.

2. Choose three values of x that are between 1 and 2:
Let's say we choose x = 1.2, 1.5, and 1.8.

For x = 1.2:
y = log3(1.2 - 1) = log3(0.2)
Calculate the logarithm base 3 of 0.2 to find the corresponding value of y for this x.

For x = 1.5:
y = log3(1.5 - 1) = log3(0.5)
Calculate the logarithm base 3 of 0.5 to find the corresponding value of y for this x.

For x = 1.8:
y = log3(1.8 - 1) = log3(0.8)
Calculate the logarithm base 3 of 0.8 to find the corresponding value of y for this x.

3. Evaluate the equation at x = 2:
For x = 2:
y = log3(2 - 1) = log3(1) = 0
The corresponding value of y is 0.

4. Now, you have the following ordered pairs:
(3, log3(2)), (4, log3(3)), (5, log3(4)) for x > 2
(1.2, log3(0.2)), (1.5, log3(0.5)), (1.8, log3(0.8)) for 1 < x < 2
(2, 0)

5. Plot those ordered pairs on a graph. On the x-axis, label the values 1, 2, 3, 4, 5. On the y-axis, label the relevant values you calculate for y.

6. The equation of the line asymptotic to the graph can be determined by observing the trend as x approaches infinity or negative infinity. In this case, since x cannot approach infinity (due to the limits of a logarithm function), there is no line asymptotic to the graph.

Remember, when evaluating logarithms, make sure the argument of the logarithm is greater than 0.