What is expand log_{10}(\sqrt[3]{x^7y^2z}) ?

The solution to expand log_{10}(\sqrt[3]{x^7y^2z}) is 2log_{10}(x)+1/3 log_{10}(xy^2z)

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expand log_{10}(\sqrt[3]{x^7y^2z})

expand

2 lo g_{10} (x) + \frac{1}{3} lo g_{10} (x y^{2} z)

Solution steps

Apply log rule:

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

Apply log rule:

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

Apply log rule:

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

Simplify

= lo g_{10} (x^{2}) + \frac{1}{3} lo g_{10} (x y^{2} z)

Apply log rule

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

assuming

x \geq 0

= 2 lo g_{10} (x) + \frac{1}{3} lo g_{10} (x y^{2} z)

Simplify

lo g_{10} (x y^{2} z) : 2 lo g_{10} (y) + lo g_{10} (x z)

= 2 lo g_{10} (x) + \frac{1}{3} (2 lo g_{10} (y) + lo g_{10} (x z))

lo g_{10} (x z) + 2 lo g_{10} (y) = lo g_{10} (x z y^{2})

= 2 lo g_{10} (x) + \frac{1}{3} lo g_{10} (x y^{2} z)

Simplify

lo g_{10} (x y^{2} z) : 2 lo g_{10} (y) + lo g_{10} (x z)

= 2 lo g_{10} (x) + \frac{1}{3} (2 lo g_{10} (y) + lo g_{10} (x z))

lo g_{10} (x z) + 2 lo g_{10} (y) = lo g_{10} (x z y^{2})

= 2 lo g_{10} (x) + \frac{1}{3} lo g_{10} (x y^{2} z)

(e^{t} + e^{3 t})^{2}

\frac{4 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

(2 - \frac{x}{16})^{9}

(2 + 3) (5 - 7)

What is expand log_{10}(\sqrt[3]{x^7y^2z}) ?
The solution to expand log_{10}(\sqrt[3]{x^7y^2z}) is 2log_{10}(x)+1/3 log_{10}(xy^2z)