simplify ln(27/36)

Solution

simplify

ln (\frac{27}{36})

3 ln (3) - 2 ln (6)

Decimal Notation

- 0.28768 \dots

Solution steps

ln (\frac{27}{36})

Apply log rule:

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

ln (\frac{27}{36}) = ln (27) - ln (36)

= ln (27) - ln (36)

ln (27) = 3 ln (3)

ln (36) = 2 ln (6)

= 3 ln (3) - 2 ln (6)

lo g_{y} (\frac{x}{4})

\frac{ln ( 2 ) - ln ( - 1 )}{9}

ln (- x) + ln (x + 1)

\frac{2}{3} lo g_{4} (74)

ln (x) + ln (x^{2} + 4)