What is expand log_{10}(x^3)ylog_{10}(x)3y ?

The solution to expand log_{10}(x^3)ylog_{10}(x)3y is 9y^2log_{10}(x)^2

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expand log_{10}(x^3)ylog_{10}(x)3y

expand

lo g_{10} (x^{3}) y lo g_{10} (x) 3 y

9 y^{2} lo g_{10} (x)^{2}

Solution steps

lo g_{10} (x^{3}) y lo g_{10} (x) \cdot 3 y

Apply log rule:

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

lo g_{10} (x^{3}) = 3 lo g_{10} (x)

= 3 lo g_{10} (x) y lo g_{10} (x) \cdot 3 y

Multiply the numbers:

3 \cdot 3 = 9

= 9 yy lo g_{10} (x) lo g_{10} (x)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

lo g_{10} (x) lo g_{10} (x) = lo g_{10} (x)^{1 + 1}

= 9 y lo g_{10} (x)^{1 + 1} y

Add the numbers:

1 + 1 = 2

= 9 y lo g_{10} (x)^{2} y

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

yy = y^{1 + 1}

= 9 lo g_{10} (x)^{2} y^{1 + 1}

Add the numbers:

1 + 1 = 2

= 9 lo g_{10} (x)^{2} y^{2}

lo g_{3} ((\frac{n ^{3}}{m})^{6})

12 ln (2 x) - tan (4 x)

- \frac{1}{5} ln (- 1) - \frac{1}{5} ln (3)

(\frac{1}{6}) \cdot ln (\frac{11.92}{8.2})

4.74472 + lo g_{10} (\frac{0.10774}{0.06322})

What is expand log_{10}(x^3)ylog_{10}(x)3y ?
The solution to expand log_{10}(x^3)ylog_{10}(x)3y is 9y^2log_{10}(x)^2