You can move the points for $x$ and $y$ on the mapping diagrams to
see how
the function values for the functions $f(x) =3^{x-2} = \frac
{3^x}{ 3^2}$
and $g(y) = \log_3(\frac y9) = log_3(y) - log_3(y)$ 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.

$\exp_3(x-2) = \frac{\exp_3(x) }{\exp_3(2)} = 3^{x-2} = \frac {3^x}{ 3^2}$ |

$\log_3(\frac y9) = log_3(y) - log_3(y)$ |

Martin Flashman, 12 Sept 2014, Created with GeoGebra