Question

Which TWO statements represent the relationship between y = 5x and y = log5 x The are the exponential and logarithmic form of the same equation They are symmetrix over the line y=0 They are symmetric over the line y=x They are inverses of one another​

Answer 1

The TWO statements that represent the relationship between y = 5x and y = log5 x are:

1. They are the exponential and logarithmic form of the same equation.
2. They are inverses of one another.

Step-by-step explanation:
The equation y = 5x is an exponential equation, while y = log5 x is a logarithmic equation. These two equations are related in that they are inverse functions of each other. In other words, if we take the logarithm of both sides of the exponential equation, we get:

log5 y = log5 5x

Using the logarithmic identity loga b^c = c loga b, we can simplify this to:

log5 y = x log5 5

Since log5 5 = 1, this further simplifies to:

log5 y = x

In other words, y = log5 x is the inverse function of y = 5x. This means that if we plug in a value for x into one equation, we can find the corresponding value of y by plugging that value into the other equation.

Also, these two equations are symmetric over the line y = x. This means that if we graph each equation on the same coordinate plane, the line y = x will be the line of symmetry for the two graphs.

Answer 2

The TWO statements that represent the relationship between y = 5x and y = log5 x are:

1. They are the exponential and logarithmic form of the same equation.

2. They are inverses of one another.

The two equations are related because they represent the same relationship between x and y, but in different forms. The first equation is an exponential equation, where y is a power of 5 raised to the x power. The second equation is a logarithmic equation, where y is the exponent to which 5 must be raised to get x.

Because the two equations represent the same relationship, they are inverses of one another. If we take the logarithm of both sides of the exponential equation, we get the logarithmic equation. If we raise 5 to both sides of the logarithmic equation, we get the exponential equation. Therefore, the two equations are inverses of one another.