simplify ln(1/(xy))

Solution

simplify

ln (\frac{1}{x y})

- (ln (x) + ln (y))

Solution steps

ln (\frac{1}{x y})

Apply log rule:

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

ln (\frac{1}{x y}) = ln (1) - ln (x y)

= ln (1) - ln (x y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (x y) = ln (x) + ln (y)

= ln (1) - (ln (x) + ln (y))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (ln (x) + ln (y))

0 - (ln (x) + ln (y)) = - (ln (x) + ln (y))

= - (ln (x) + ln (y))

lo g_{10} (\frac{π r ^{3} h}{3})

ln (2 \cdot x_{1} x_{2} x_{3})

- 3 ln (x) - 2 ln (y)

2 ln (3 x - 8) - ln (5 x + 1)

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