Laws of Logs

operation

law of indices

law for logs

multiplication

a^x x a^y = a^x+y

log_a xy = log_a x + log_a y

division

a^x / a^y = a^x-y

log_a x/y = log_a x - log_a y

powers

(a^x)ⁿ = a^nx

log_a xⁿ = nlog_a x

roots

(a^x)^1/n = a^x/n

log_{a write later}

reciprocals

1/a^x = a^-x

log_a 1/x = log_a 1 - log_a x = -log_a x