You can move the points for $x$ and $y$ on the mapping diagrams to
see how
the function values for the functions $f(x) = 3^{2+x} = 3^2 \cdot
3^x $
and $g(y) = \log_3(9y) = log_3(9) + log_3(y)$ change on the
diagrams with the different procedures applied in the prescribed orders.

You can change the base as well as the values of $a$ and $b$ using the sliders.

$\exp_3(2+x) = \exp_3(2) \cdot \exp_3(x) = 3^{2+x} = 3^2 \cdot 3^x$ |

$\log_3(9y) = log_3(9) + log_3(y)$ |

Martin Flashman, 12 Sept 2014, Created with GeoGebra