simplify ln((xy)/x)

Solution

simplify

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

ln (y)

Solution steps

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

Apply log rule:

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

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

= ln (x y) - ln (x)

Apply log rule:

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

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

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

Simplify

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

= ln (y)

3 ln (\frac{x}{x + 1})

lo g_{10} (e^{- x} cos (π x))

2 - 2 ln (2) + 2 ln (x)

lo g_{10} (810) + lo g_{10} (0.03)

- \frac{1}{3} (ln (26) - ln (5))