Logarithms
A logarithm asks: what power do I raise the base to, to get this number?
A worked example
log₂ 32 = 5 because 2⁵ = 32. To solve 1.06ᵗ = 2, take logs: t = log 2 / log 1.06 = 11.9.
The mistake people actually make
log(a) − log(b) is log(a/b), not log(a) / log(b). Isolate the power before taking logs.