simplify ln(100/40)

Solution

simplify

ln (\frac{100}{40})

2 ln (10) - ln (40)

Decimal Notation

0.91629 \dots

Solution steps

ln (\frac{100}{40})

Apply log rule:

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

ln (\frac{100}{40}) = ln (100) - ln (40)

= ln (100) - ln (40)

ln (100) = 2 ln (10)

= 2 ln (10) - ln (40)

ln (\frac{95 x 1 0 ^{12} ( 2.5 )}{1 0 ^{- 3}})

500 + 47 ln (112) - 47 ln (212)

ln (1.7708) + 0.6 \cdot ln (1.275)

\frac{π}{4} ln (3)

\frac{4}{5} ln (22950)