simplify ln(8/13)

Solution

simplify

ln (\frac{8}{13})

3 ln (2) - ln (13)

Decimal Notation

- 0.48550 \dots

Solution steps

ln (\frac{8}{13})

Apply log rule:

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

ln (\frac{8}{13}) = ln (8) - ln (13)

= ln (8) - ln (13)

ln (8) = 3 ln (2)

= 3 ln (2) - ln (13)

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

lo g_{10} (\frac{z ^{4}}{5})

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

- lo g_{10} (8.4 \cdot 1 0^{- 4})

lo g_{10} (\frac{x ^{2} y ^{18}}{z ^{8}})