When $b \ne 1$ , the values of the function $exp_b$ and $log_b$ vary in predictable ways depending on whether $b>1$ or $0<b<1$.

This is apparent by reviewing the mapping diagrams along with the graphs in some of our previous examples.

But first we review the key concepts: increasing and decreasing.

Notice how the graph and mapping diagram visualize the fact that for exponential and logarithmic functions, if $b >1$ then $exp_b$ and $log_b$ are increasing functions while if $0<b<1$ then $exp_b$ and $log_b$ are decreasing functions.

You can use this next dynamic example to investigate visually the effects of the base $b$ simultaneously on the exponential and logarithmic functions whether the functions are increasing or decreasing in a mapping diagram and a graph.