Logarithms
A log asks: what exponent gets me there?
Concept
Logs undo exponents
log_b(n) = e means exactly b^e = n. Reading it out loud as 'what power of b gives n' makes most log problems trivial.
The laws follow from exponent laws: products become sums, quotients become differences, powers come out front.
log_b(xy) = log_b x + log_b y · log_b(x^k) = k·log_b x