1. Sketch the curve

   $$y={\log }_2(x)$$

   giving the coordinates of any point of intersection with the coordinate axes.

2. Show that

   $${\log }_{\frac{1}{2}}(x)=-{\log }_2(x)$$

   and hence sketch the curve

   $$y={\log }_{\frac{1}{2}}(x)$$

For part (a), note that ${\log }_2(x)$ is the inverse function of $2^x.$

For part (b), write

and rearrange to show that

To sketch $y=-f(x),$ we reflect $y=f(x)$ in the $x$ axis.