Answer
No.
Work Step by Step
Every point in the Y-axis has an $x$ coordinate equal to $0$.
To find the x-intercept in $y = log_2x$, you have to make $x = 0$.
Doing as above, we have $y = log_20 \longrightarrow 2^{y} = 0$, but there is no $y$ value that satisfies this expression. Therefore there is not an x-intercept in the function $y = log_2x$.
