What is ln((xsqrt(y))/(y^3)) ?

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

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simplify ln((xsqrt(y))/(y^3))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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)

3 ln (a) + 6 ln (b) - ln (8)

lo g_{10} (0^{'} 1)

lo g_{x} (\frac{a ^{3} b}{c})

- lo g_{10} (6.28 \cdot 1 0^{- 5})

lo g_{10} (4 x) - lo g_{10} (12 + x)

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