simplify 4ln(4/10)

Solution

simplify

4 ln (\frac{4}{10})

4 (2 ln (2) - ln (10))

Decimal Notation

- 3.66516 \dots

Solution steps

4 ln (\frac{4}{10})

Apply log rule:

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

ln (\frac{4}{10}) = ln (4) - ln (10)

= 4 (ln (4) - ln (10))

ln (4) = 2 ln (2)

= 4 (2 ln (2) - ln (10))

\frac{- ln ( 2 ) - 5 ln ( x ) - 5}{x}

\frac{1}{4} ln (\frac{7}{2})

2 lo g_{10} (x) + lo g_{10} (5 x - 8)

ln (\frac{cos ( x ^{2} )}{x})

lo g_{e} (\frac{1}{4}) - lo g_{e} (4)