What is 4+3log_{a}(x)-log_{a}(\sqrt[5]{yz}) ?

The solution to 4+3log_{a}(x)-log_{a}(\sqrt[5]{yz}) is 4+log_{a}((x^3(yz)^{4/5})/(yz))

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simplify 4+3log_{a}(x)-log_{a}(\sqrt[5]{yz})

simplify

4 + lo g_{a} (\frac{x ^{3} ( yz ) ^{\frac{4}{5}}}{yz})

Solution steps

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{a} (x) = lo g_{a} (x^{3})

Apply log rule:

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

Simplify

= 4 + lo g_{a} (\frac{x ^{3} ( yz ) ^{\frac{4}{5}}}{yz})

ln (\frac{2 a ^{3}}{b ^{4}})

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

ln ((cos (x))^{2})

ln (\frac{5 x ^{7}}{y})

3 \cdot ln (5) - 3 \cdot ln (2)

What is 4+3log_{a}(x)-log_{a}(\sqrt[5]{yz}) ?
The solution to 4+3log_{a}(x)-log_{a}(\sqrt[5]{yz}) is 4+log_{a}((x^3(yz)^{4/5})/(yz))