What is ln((\sqrt[5]{x^2yz})/(b^2w^{1/2)}) ?

The solution to ln((\sqrt[5]{x^2yz})/(b^2w^{1/2)}) is ln(\sqrt[5]{x^2yz})-2ln(b)-1/2 ln(w)

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simplify ln((\sqrt[5]{x^2yz})/(b^2w^{1/2)})

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)

ln (b^{2} w^{\frac{1}{2}}) = ln (b^{2}) + ln (w^{\frac{1}{2}})

Apply log rule:

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

ln (b^{2}) = 2 ln (b)

Apply log rule:

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

ln (w^{\frac{1}{2}}) = \frac{1}{2} ln (w)

- (2 ln (b) + \frac{1}{2} ln (w)) : - 2 ln (b) - \frac{1}{2} ln (w)

ln ((sin (x))^{x})

lo g_{10} (\frac{x ^{3} y ^{2}}{z})

lo g_{b} (\frac{x ^{2} y}{z ^{4}})

lo g_{6} (x^{4} y^{6})

ln (x^{2} y)

What is ln((\sqrt[5]{x^2yz})/(b^2w^{1/2)}) ?
The solution to ln((\sqrt[5]{x^2yz})/(b^2w^{1/2)}) is ln(\sqrt[5]{x^2yz})-2ln(b)-1/2 ln(w)