simplify ln(32/125)

Solution

simplify

ln (\frac{32}{125})

5 ln (2) - 3 ln (5)

Decimal Notation

- 1.36257 \dots

Solution steps

ln (\frac{32}{125})

Apply log rule:

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

ln (\frac{32}{125}) = ln (32) - ln (125)

= ln (32) - ln (125)

ln (32) = 5 ln (2)

ln (125) = 3 ln (5)

= 5 ln (2) - 3 ln (5)

\frac{1}{9} \cdot lo g_{2} (\frac{1}{9}) + \frac{8}{9} \cdot lo g_{2} (\frac{8}{9})

lo g_{10} (\frac{- 7 ^{3} 6 ^{9}}{- 7 ^{2}})

ln (\frac{1}{n + 1})

- \frac{3}{5} \cdot lo g_{2} (\frac{3}{5}) - \frac{2}{5} lo g_{2} (\frac{2}{5})

2 lo g_{10} (x) + 3 lo g_{10} (y) - lo g_{10} (x)