Can anyone help? I have a test and this is the last question I need answered. I'm lost and exhausted! Thanks for any help!

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

Of course, I'd be happy to help you with this question! To evaluate the logarithmic equation for different values of x, we can substitute the values of x into the equation and simplify the expression.

First, let's consider three values of x that are greater than 1. We need to plug these values into the equation y = log7(x) and calculate the corresponding values of y. For example, let's use x = 2:

y = log7(2)

To evaluate this logarithm, we need to determine what power of 7 gives us 2. In other words, we ask ourselves, "What is the exponent we need to raise 7 to in order to get 2?" To find the answer, we can rewrite the equation as:

7^y = 2

Now, we can solve for y by taking the logarithm base 7 on both sides:

log7(7^y) = log7(2)

The logarithm base 7 "undoes" the exponentiation, giving us:

y = log7(2)

Using a calculator or computer software, we can find the value of this logarithm to be approximately 0.3562.

Similarly, you can choose two more values greater than 1, such as x = 3 and x = 10, and repeat the process to find their corresponding values of y.

Next, let's consider three values of x that are between 0 and 1. Let's say x = 0.5:

y = log7(0.5)

Following the same steps as before, we rewrite the equation as:

7^y = 0.5

Taking the logarithm base 7 on both sides and using a calculator, we find that y is approximately -0.3562.

Repeat this process for two more values between 0 and 1, such as x = 0.1 and x = 0.01, to find their corresponding values of y.

Finally, when x = 1, we have:

y = log7(1)

Since any number raised to the power of 0 equals 1, the logarithm of 1 to any base is always 0. Therefore, y = 0 when x = 1.

By evaluating the logarithmic equation for these different values of x, we can find the corresponding values of y. Remember to use a calculator or computer software when calculating logarithms. Good luck with your test!