Change of Base Law (Leaving Cert Mathematics): Flashcards

Rewriting a log with one base using logs with a different base

Calculators only support base 10 ($log$) or base e ($ln$)

$\log_b x = \frac{\log_a x}{\log_a b}$

Original base

New base

Argument of the logarithm

$a = 10$ (common log) or $a = e$ (natural log)

Change the bigger base

$2$

$x = 8$

$x = \frac{1}{8}$

$\frac{\log_2 x}{\log_2 4}$