Which statements represent the relationship between y=3x and y=log3x?

Select each correct answer.

The functions are inverses of each other.

The graphs of functions are symmetric to each other over the line y = x.

The equation y=log3x is the logarithmic form of y=3x .

The graphs of functions are symmetric about the line y = 0.

Let's see if the functions are inverse of each other. Taking inverse of both equations we have.

Y^ (-1) = (3x) ^ (-1) = 1 / (3x)

But from the second eqn, y = log3x, we have,

Y^ (-1) = (log3x) ^ (-1)

Recall, if N = a^ (x)

Then log_a N = x

Let N = Y^ (-1), a = log (3x) and x = (-1)

Then log_log (3x) Y^ (-1) = - 1.

Then Y^ (-1) = (Log3x) ^ (-1) = 1 / (log3x). I would say the equation ​ y=log3x ​ is the logarithmic form of ​ y=3x ​.