Which statements represent the relationship between y=2x and y=log2x ?
Select each correct answer.
The equation y=log2x is the logarithmic form of y=2x . <my choice
The graphs of the functions are symmetric to each other over the line y = x.
The graphs of the functions are symmetric about the line y = 0.
The functions are inverses of each other. <my choice
plus, since they are inverses, (b) is also correct.
your answer is correct if you meant
y = 2x
y = log2x
The correct statements that represent the relationship between y=2x and y=log2x are:
- The equation y=log2x is the logarithmic form of y=2x .
- The functions are inverses of each other.
To determine the relationship between the equations y=2x and y=log2x, let's analyze each statement:
1. The equation y=log2x is the logarithmic form of y=2x.
This statement is correct. The equation y=log2x is the logarithmic expression of y=2x, specifically in base 2. The logarithmic form highlights the exponent (logarithm) to which the base (2) must be raised to obtain the value of x.
2. The graphs of the functions are symmetric to each other over the line y = x.
This statement is not correct. The graphs of y=2x and y=log2x are not symmetric to each other over the line y = x. In fact, if you were to graph these equations, you would see that they are different.
3. The graphs of the functions are symmetric about the line y = 0.
This statement is not correct. The graphs of y=2x and y=log2x are not symmetric about the line y = 0. Again, if you were to graph these equations, you would notice that they have different shapes.
4. The functions are inverses of each other.
This statement is correct. In mathematics, two functions are considered inverses of each other if applying one function and then the other returns the original input. In this case, y=2x and y=log2x are inverses of each other. If you substitute y=2x into y=log2x (or vice versa), you will get the original input x.
In summary, the correct statements that represent the relationship between y=2x and y=log2x are:
- The equation y=log2x is the logarithmic form of y=2x.
- The functions are inverses of each other.