simplify ln((xy)/e)

Solution

simplify

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

ln (x) + ln (y) - 1

Solution steps

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

Apply log rule:

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

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

= ln (x y) - ln (e)

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 (e)

Apply log rule:

lo g_{a} (a) = 1

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

lo g_{b} ((x y)^{3})

4 lo g_{10} (a) + lo g_{10} (b)

ln (\frac{5 \cdot 8 ^{5}}{2.9})

ln (8 e^{- 300 t})

ln (\frac{m ^{3}}{n})