What is expand log_{10}(\sqrt[4]{(y^3)/(20x^5)}) ?

The solution to expand log_{10}(\sqrt[4]{(y^3)/(20x^5)}) is 1/4 (3log_{10}(y)-log_{10}(20x^5))

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expand log_{10}(\sqrt[4]{(y^3)/(20x^5)})

expand

\frac{1}{4} (3 lo g_{10} (y) - lo g_{10} (20 x^{5}))

Solution steps

Rewrite as

= lo g_{10} ((\frac{y ^{3}}{20 x ^{5}})^{\frac{1}{4}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{4} lo g_{10} (\frac{y ^{3}}{20 x ^{5}})

Simplify

lo g_{10} (\frac{y ^{3}}{20 x ^{5}}) : 3 lo g_{10} (y) - lo g_{10} (20 x^{5})

= \frac{1}{4} (3 lo g_{10} (y) - lo g_{10} (20 x^{5}))

lo g_{10} (20 x^{5}) = lo g_{10} (20) + 5 lo g_{10} (x)

= \frac{1}{4} (3 lo g_{10} (y) - (5 lo g_{10} (x) + lo g_{10} (20)))

lo g_{10} (20) + 5 lo g_{10} (x) = lo g_{10} (20 x^{5})

= \frac{1}{4} (3 lo g_{10} (y) - lo g_{10} (20 x^{5}))

lo g_{10} (20 x^{5}) = lo g_{10} (20) + 5 lo g_{10} (x)

= \frac{1}{4} (3 lo g_{10} (y) - (5 lo g_{10} (x) + lo g_{10} (20)))

lo g_{10} (20) + 5 lo g_{10} (x) = lo g_{10} (20 x^{5})

= \frac{1}{4} (3 lo g_{10} (y) - lo g_{10} (20 x^{5}))

4.8 (0.5 d + \frac{a - b}{2.4})

\frac{\partial}{\partial x} ((z) (x^{2} e^{y} + 10 y))

(2 + 4 i)^{3}

\frac{4 ( 6 + 3 )}{33}

- 2 (2 + 34)

What is expand log_{10}(\sqrt[4]{(y^3)/(20x^5)}) ?
The solution to expand log_{10}(\sqrt[4]{(y^3)/(20x^5)}) is 1/4 (3log_{10}(y)-log_{10}(20x^5))