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. y = -log(sub)3 (x - 1)
I don't know if I did this right, I changed it to -3^y=x-1. I am having difficulty replacing x and finding out what y is. I would have an easier time if I was substituting y and finding x. What am I doing wrong. Thanks!!
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To evaluate the logarithmic equation y = -log₃(x - 1) for different values of x, you need to substitute those values into the equation and calculate the corresponding values of y.
Let's break it down into three cases:
1. Values of x that are greater than 2:
- Take three values greater than 2, for example, x = 3, 4, and 5.
- Substitute each value of x into the equation: y = -log₃(x - 1).
- Calculate the values of y for each x: y₁ = -log₃(3 - 1), y₂ = -log₃(4 - 1), and y₃ = -log₃(5 - 1).
- Calculate y using the logarithmic properties: y = -log₃(2), y = -log₃(3), and y = -log₃(4).
2. Values of x that are between 1 and 2:
- Choose three values between 1 and 2, for example, x = 1.1, 1.5, and 1.9.
- Substitute each value of x into the equation: y = -log₃(x - 1).
- Calculate the values of y for each x: y₁ = -log₃(1.1 - 1), y₂ = -log₃(1.5 - 1), and y₃ = -log₃(1.9 - 1).
- Evaluate y using the logarithmic properties: y = -log₃(0.1), y = -log₃(0.5), and y = -log₃(0.9).
3. For x = 2:
- Replace x with 2 in the equation: y = -log₃(2 - 1).
- Simplify the expression: y = -log₃(1).
Now, let's correct the step where you tried changing the equation to -3^y = x - 1. The original equation y = -log₃(x - 1) is in logarithmic form, and the expression -3^y = x - 1 is in exponential form. It is essential to work with the correct form of the equation to find accurate results.
By following the steps outlined above, you should be able to correctly substitute values of x to find the corresponding values of y for the given logarithmic equation.