What is ln((sqrt(x))/(y^3)) ?

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

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simplify ln((sqrt(x))/(y^3))

simplify

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

ln (x) - 3 ln (y)

Solution steps

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

Apply log rule:

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

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

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

ln (\frac{4 - x}{2 + 2 x})

ln (\frac{3 x}{x + 2})

3 ln (x) + \frac{1}{3} ln (x + 2)

ln (x^{3} yz)

2 + 3 ln (t) - 4 ln (x)

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