Question

Which of the following is a logarithmic function? A. Y=0.25X B. Y=x^0.25 c.y=log25^x d.y=(0.25)^x

Answer 1

The correct option is C .

Explanation:

A logarithm function is written in the form of
`y=log_ax`,

Since, y = 0.25x is the type of function y = mx + c,

Which is the general form of a linear function,

⇒ y = 0.25x is not a logarithm function,

`y=x^(0.25)` is the type of function
`y=kx^a`, where k and a are any real number,

Which is the general form of a power function,

⇒
`y=x^(0.25)` is not a logarithmic function.

`y=(0.25)^x` is the type of function
`y=ab^x`

Which is the general form of exponential function,

⇒
`y=(0.25)^x` is not a logarithmic function,

Hence, only the function in option C has written in the form of
`y=log_ax`.

Option C is correct.

Answer 2

I think the answer is C, y= log 25^x. Logarithmic functions are inverses of exponential functions. the inverse of exponential function y =a ^x is x = a^y. The logarithmic function y = logaX, is defined to be equivalent to the exponential equation x= a^y.