simplify ln(8/15)

Solution

simplify

ln (\frac{8}{15})

3 ln (2) - ln (15)

Decimal Notation

- 0.62860 \dots

Solution steps

ln (\frac{8}{15})

Apply log rule:

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

ln (\frac{8}{15}) = ln (8) - ln (15)

= ln (8) - ln (15)

ln (8) = 3 ln (2)

= 3 ln (2) - ln (15)

\frac{ln ( \frac{5}{7} )}{10 ln ( 3 )}

lo g_{3} (27 (x - 4)^{3})

4 (ln (7) - 2 ln (2)) - \frac{3}{7}

ln (\frac{2 ^{n}}{( 2 + n ) ^{\frac{3}{4}}})

0.7 ln (\frac{0.7 m}{p}) + 0.3 ln (\frac{0.3 m}{b})