Logarithms (Leaving Cert Applied Maths): Flashcards

Reverse operation of raising numbers to powers

$a^m = n \leftrightarrow \log_a n = m$

The base (must be positive and not equal to 1)

The power or index

$\log_a(xy) = \log_a x + \log_a y$

$\log_a(\frac{x}{y}) = \log_a x - \log_a y$

$\log_a(x^p) = p \log_a x$

$\log_a(a^x) = x$

If $\log_a b = \log_a c$, then $b = c$

$\ln$ (instead of $\log_e$)

$e$ (approximately 2.718)

Only defined for positive arguments