What is ln((xy)/((y-x)^3)) ?

The solution to ln((xy)/((y-x)^3)) is ln(x)+ln(y)-3ln(y-x)

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simplify ln((xy)/((y-x)^3))

simplify

ln (\frac{x y}{( y - x ) ^{3}})

ln (x) + ln (y) - 3 ln (y - x)

Solution steps

ln (\frac{x y}{( y - x ) ^{3}})

Apply log rule:

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

ln (\frac{x y}{( y - x ) ^{3}}) = ln (x y) - ln ((y - x)^{3})

= ln (x y) - ln ((y - x)^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((y - x)^{3}) = 3 ln (y - x)

= ln (x y) - 3 ln (y - 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) - 3 ln (y - x)

ln (\frac{4.5}{15})

ln (255 \cdot 1 0^{22})

ln (x) + ln (6 x)

ln (4^{x}) + ln (2^{x + 2})

7 ln (- \frac{1}{3} ln (y))

What is ln((xy)/((y-x)^3)) ?
The solution to ln((xy)/((y-x)^3)) is ln(x)+ln(y)-3ln(y-x)