simplify 6+3ln(1/2)

Solution

simplify

6 + 3 ln (\frac{1}{2})

6 - 3 ln (2)

Decimal Notation

3.92055 \dots

Solution steps

6 + 3 ln (\frac{1}{2})

Apply log rule:

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

ln (\frac{1}{2}) = ln (1) - ln (2)

= 6 + 3 (ln (1) - ln (2))

3 (ln (1) - ln (2)) = - 3 ln (2)

= 6 - 3 ln (2)

lo g_{2} (\frac{c d ^{3}}{e ^{4}})

lo g_{10} (8^{2}) - lo g_{10} (12 5^{2})

lo g_{10} (3 (x + 1)^{2})

ln (x) - ln (x + 1)

9 ln (x) - \frac{1}{5} ln (y)