simplify ln(9/32)

Solution

simplify

ln (\frac{9}{32})

2 ln (3) - 5 ln (2)

Decimal Notation

- 1.26851 \dots

Solution steps

ln (\frac{9}{32})

Apply log rule:

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

ln (\frac{9}{32}) = ln (9) - ln (32)

= ln (9) - ln (32)

ln (9) = 2 ln (3)

ln (32) = 5 ln (2)

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

- lo g_{10} (3.6 \cdot 1 0^{- 9})

ln (\frac{x}{5 + x})

ln (20000000) - ln (300000)

2 ln (4) - ln (6) + 3 ln (2)

- lo g_{10} (2.09 (1 0^{- 12}))