Logarithms invert exponentials

The function [3nd $\log_b(\cdot)$] inverts the function $b^{(\cdot)}.$ In other words, $\log_b(n) = x$ implies that $b^x = n,$ so $\log_b(b^x)=x$ and $b^{\log_b(n)}=n.$ (For example, $\log_2(2^3) = 3$ and $2^{\log_2(8)} = 8.$) Thus, logarithms give us tools for analyzing anything that grows exponentially. If a population of bacteria grows exponentially, then logarithms can be used to answer questions about how long it will take the population to reach a certain size. If your wealth is accumulating interest, logarithms can be used to ask how long it will take until you have a certain amount of wealth. (TODO)