What is expand log_{3}(x^5y^3) ?

The solution to expand log_{3}(x^5y^3) is 5log_{3}(x)+3log_{3}(y)

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expand log_{3}(x^5y^3)

expand

lo g_{3} (x^{5} y^{3})

5 lo g_{3} (x) + 3 lo g_{3} (y)

Solution steps

lo g_{3} (x^{5} y^{3})

Apply log rule:

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

lo g_{3} (x^{5} y^{3}) = lo g_{3} (x^{5}) + lo g_{3} (y^{3})

= lo g_{3} (x^{5}) + lo g_{3} (y^{3})

Apply log rule:

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

lo g_{3} (x^{5}) = 5 lo g_{3} (x)

= 5 lo g_{3} (x) + lo g_{3} (y^{3})

Apply log rule:

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

lo g_{3} (y^{3}) = 3 lo g_{3} (y)

= 5 lo g_{3} (x) + 3 lo g_{3} (y)

ln (\frac{134.8}{15})

- ln (x y^{2})

\frac{1}{4} lo g_{10} (2)

- 2 ln (\frac{1}{2})

ln (\frac{e ^{2}}{17})

What is expand log_{3}(x^5y^3) ?
The solution to expand log_{3}(x^5y^3) is 5log_{3}(x)+3log_{3}(y)