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
They are inverses of each other.
They are symmetric about the line y = x. <<my choice
They are symmetric about the line y = 0.
I think you have a typo and you wanted to compare
y = 2^x with y = log2 x
They are inverses of each other.
Proof:
start with y = 2^x
the inverse is formed by interchanging the x and y's
----> x = 2^y
which in log form would be : y = y = log2 x
To determine the relationship between the equations y=2x and y=log2x, we can analyze their properties.
1. The equation y=log2x is the logarithmic form of y=2x.
This statement is correct. The equation y=log2x is the logarithmic form of y=2x because it expresses the exponent (2x) in terms of logarithm (log2x).
2. They are inverses of each other.
This statement is NOT correct. Two functions are inverses when they "undo" each other's operations. In the given equations, y=2x is an exponential function, while y=log2x is a logarithmic function. Exponential and logarithmic functions are not inverses of each other.
3. They are symmetric about the line y = x.
This statement is correct. The line y = x is the diagonal line that cuts the coordinate plane into two equal halves at a 45-degree angle. The equations y=2x and y=log2x have this line of symmetry because swapping the x and y variables while keeping the equation true reflects the point across the line y = x.
4. They are symmetric about the line y = 0.
This statement is NOT correct. The line y = 0 represents the x-axis, and the equations y=2x and y=log2x do not have symmetry about this line.
So, the correct statements are:
- The equation y=log2x is the logarithmic form of y=2x.
- They are symmetric about the line y = x.