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

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

simplify

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)

6 lo g_{10} (3) - 4 lo g_{10} (2)

4 lo g_{2} (x) + lo g_{2} (y)

2 lo g_{10} (a) + 2 lo g_{10} (b)

lo g_{4} (17 x)

lo g_{3} (\frac{z}{27})

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