We have the following:
[tex]f(x)=8^x[/tex]
(a)
for there to be an upward displacement, we must add the function the value that we want it to rise, like this
[tex]f(x)=8^x+5[/tex]
(b)
for there to be a shift to the left, we must add the exponent from the value we want it to rise, like this
[tex]f(x)=8^{x+9}[/tex]
(c)
for there to be a shift to the left, we must subtract the exponent from the value we want it to rise, like this
The inverse is:
[tex]\begin{gathered} y=8^x \\ x=8^y \\ \ln x=y\cdot\ln 8 \\ y=\frac{\ln x}{\ln 8} \end{gathered}[/tex]
The answer is
[tex]f(x)=\frac{\ln x}{\ln 8}[/tex]
