Evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Show your work.

y=log7 x

To evaluate the logarithmic equation for different values of x, we need to substitute those values into the equation and calculate the corresponding value of y.

1. For three values of x greater than 1:
Let's choose x = 2, 5, and 10.

For x = 2:
y = log7(2)
You can use a calculator to solve this. If you don't have one, use the formula: y = logb(x) = log(x) / log(b)
Using a calculator, y ≈ 0.9456.

For x = 5:
y = log7(5) ≈ 0.8451.

For x = 10:
y = log7(10) ≈ 1.1833.

Therefore, the values of y for x = 2, 5, and 10 are approximately 0.9456, 0.8451, and 1.1833, respectively.

2. For three values of x between 0 and 1:
Let's choose x = 0.2, 0.5, and 0.8.

For x = 0.2:
y = log7(0.2)
Using the formula, y ≈ -0.8451.

For x = 0.5:
y = log7(0.5) ≈ -0.4314.

For x = 0.8:
y = log7(0.8) ≈ -0.1340.

Therefore, the values of y for x = 0.2, 0.5, and 0.8 are approximately -0.8451, -0.4314, and -0.1340, respectively.

3. At x = 1:
y = log7(1)
The logarithm of 1 to any base is always 0.
Therefore, y = 0 at x = 1.

So, the values of y for x > 1 are approximately 0.9456, 0.8451, and 1.1833. The values of y for 0 < x < 1 are approximately -0.8451, -0.4314, and -0.1340. And y = 0 when x = 1.