simplify ln(r/(8s))

Solution

simplify

ln (\frac{r}{8 s})

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

Solution steps

ln (\frac{r}{8 s})

Apply log rule:

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

ln (\frac{r}{8 s}) = ln (r) - ln (8 s)

= ln (r) - ln (8 s)

Apply log rule:

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

ln (8 s) = ln (8) + ln (s)

= ln (r) - (ln (s) + ln (8))

ln (8) = 3 ln (2)

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

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

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

lo g_{2} (9) + lo g_{2} (5)

lo g_{2} (x^{4} y^{3})

lo g_{b} (\frac{1}{8})

ln (yz)

lo g_{2} (\frac{s ^{9}}{5 t ^{2}})