What is expand ln((y^3x^6)/((\sqrt[3]{z^2))w^4}) ?

The solution to expand ln((y^3x^6)/((\sqrt[3]{z^2))w^4}) is 3ln(y)+6ln(x)-ln(\sqrt[3]{z^2})-4ln(w)

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expand ln((y^3x^6)/((\sqrt[3]{z^2))w^4})

expand

Solution steps

Apply log rule:

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

Apply log rule:

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

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

Apply log rule:

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

ln (x^{6}) = 6 ln (x)

Apply log rule:

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

ln (w^{4}) = 4 ln (w)

lo g_{10} (z x^{5})

lo g_{10} (\frac{y ^{5}}{z})

lo g_{2} ((5 x^{3} - 2) (x^{2} - 1)^{3})

lo g_{3} (100) - lo g_{3} (18) + lo g_{3} (50)

ln (\frac{( x ^{2} - 1 )}{x ^{5}})

What is expand ln((y^3x^6)/((\sqrt[3]{z^2))w^4}) ?
The solution to expand ln((y^3x^6)/((\sqrt[3]{z^2))w^4}) is 3ln(y)+6ln(x)-ln(\sqrt[3]{z^2})-4ln(w)