What is ln((sqrt(xy^4))/(z^3)) ?

The solution to ln((sqrt(xy^4))/(z^3)) is ln(sqrt(x)sqrt(y^4))-3ln(z)

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simplify ln((sqrt(xy^4))/(z^3))

simplify

ln (\frac{x y ^{4}}{z ^{3}})

ln (x y^{4}) - 3 ln (z)

Solution steps

ln (\frac{x y ^{4}}{z ^{3}})

Apply log rule:

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

ln (\frac{x y ^{4}}{z ^{3}}) = ln (x y^{4}) - ln (z^{3})

= ln (x y^{4}) - ln (z^{3})

Apply log rule:

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

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

= ln (x y^{4}) - 3 ln (z)

x y^{4} = x y^{4}

= ln (x y^{4}) - 3 ln (z)

ln \frac{( ( x + a ) ^{2} + y ^{2} )}{( ( x - a ) ^{2} + y ^{2} )}

lo g_{e} (\frac{3}{4} ln x^{2} + 2 + \frac{1}{2} ln ∣ x ∣)

ln (\frac{6}{5}) - ln (\frac{4}{6})

3 ln (\frac{5}{2}) + \frac{9}{10}

- \frac{1}{5} ln (x) - 5 [ln (y) - 3 ln (z)]

What is ln((sqrt(xy^4))/(z^3)) ?
The solution to ln((sqrt(xy^4))/(z^3)) is ln(sqrt(x)sqrt(y^4))-3ln(z)