Algebra - How can I graph this function and work with exponential function with base $a$?

The graph $f(x)=5(0.5)^{−x}$ is a reflection of the graph $g(x)=5(0.5)^x$ in the $y$-axis.

To find the reflection of $f(x)$ in the line $y=x$, ie its inverse, we make $x$ the subject:

$$y=5(0.5)^{−x}implies 0.5^{-x}=frac{y}{5}implies 2^x=frac{y}{5}implies x =log_2 frac{y}{5}$$ So, where $h(x)$ is the inverse function: $$h(x)=log_2 frac{x}{5}$$ Now, for the last part: Using log and exponential laws: $$a^x=e^{ln{a^x}}=e^{xln a}$$ as required.