Question

Which of the following explains why f(x) = log2x

Answer 1

Answer:

• There is no power of 2 that is equal to 0.

• Its inverse does not have any x-intercepts.

Step-by-step explanation:

Given the function

$\:\:f\left(x\right)=\log \:_2\left(x\right)$

This function can be written as:

$y=\log _2\left(x\right)$

As the rule tells s that

$\:y=log_ax\Rightarrow \:a^y=x$

so

$x=2^y\:\:$

As we know that the value of x=0 at y-intercept.

$0=2^y\:\:$

For any value of $y$, this statement is false as there is no power of 2 that is equal to 0.

Also

Lets interchange x and y in the equation $x=2^y\:\:$  to find the inverse of the function.

$y=2^x\:\:$

So, it doesn't have any x-intercepts as for any value of x, the value of $y$ can not be zero for this function.

Therefore, Its inverse does not have any x-intercepts.