Logarithm Expressions and Equations (HSC SSCE Mathematics Advanced): Flashcards

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

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

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

They must have the same base

Evaluates to a rational number (expressible as a fraction)

Evaluates to irrational number (non-repeating, non-terminating)

All arguments must be positive ($x > 0$)

$a^y = x$

$x = \frac{\log_c(b)}{\log_c(a)}$

Solutions making arguments negative or zero must be rejected