Logarithmic Function Manipulation

In 2.9 we found that Nova reaches 10,000 subscribers at $t = \log_{1.5} 39.0625$, somewhere between 9 and 10, but no calculator has $a \log_{1.5}$ key. This note gives the rules that let you rearrange logarithms. One of them, the change of base formula, finally lets you compute that number.