Laws of Logarithms (AQA A-Level Mathematics): Flashcards

$\log(a) + \log(b) = \log(ab)$

$\log(a) - \log(b) = \log\left(\frac{a}{b}\right)$

$b \log(a) = \log(a^b)$

$2^{x+3}$ (add the powers)

$2^{x-y}$ (subtract the powers)

$1$

$\log(3) + 2\log(a) + 3\log(b)$

$\log(10) = 1$

Unlogging each term separately; must combine logs first

Gather logs into one: $\log\left(\frac{x-5}{x}\right) = 7$