simplify ln(r/(9s))

Solution

simplify

ln (\frac{r}{9 s})

ln (r) - 2 ln (3) - ln (s)

Solution steps

ln (\frac{r}{9 s})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{r}{9 s}) = ln (r) - ln (9 s)

= ln (r) - ln (9 s)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (9 s) = ln (9) + ln (s)

= ln (r) - (ln (s) + ln (9))

ln (9) = 2 ln (3)

= ln (r) - (ln (s) + 2 ln (3))

- (2 ln (3) + ln (s)) : - 2 ln (3) - ln (s)

= ln (r) - 2 ln (3) - ln (s)

ln (\frac{x ^{5}}{y ^{2}})

1 - lo g_{2} (\frac{k - 1}{k})

ln (\frac{1}{v})

lo g_{4} (2 x + 1) - lo g_{4} (3 y + 4)