Logarithms in Math 30-1
log_b(x) asks what power of b gives x, so log_b(x) = y and b^y = x say exactly the same thing.
A worked example
log₃ 81 = 4 because 3^4 = 81. To solve 1.05^t = 3, take logs: t = log 3 / log 1.05 = 22.5.
The mistake people actually make
log(A x B) is log A + log B, not log A x log B. The log of 1 is 0 for every base, and the log of the base itself is 1.