What is expand log_{5}(x^3y^2) ?

The solution to expand log_{5}(x^3y^2) is 3log_{5}(x)+2log_{5}(y)

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expand log_{5}(x^3y^2)

expand

lo g_{5} (x^{3} y^{2})

3 lo g_{5} (x) + 2 lo g_{5} (y)

Solution steps

lo g_{5} (x^{3} y^{2})

Apply log rule:

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

lo g_{5} (x^{3} y^{2}) = lo g_{5} (x^{3}) + lo g_{5} (y^{2})

= lo g_{5} (x^{3}) + lo g_{5} (y^{2})

Apply log rule:

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

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

= 3 lo g_{5} (x) + lo g_{5} (y^{2})

Apply log rule:

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

lo g_{5} (y^{2}) = 2 lo g_{5} (y)

= 3 lo g_{5} (x) + 2 lo g_{5} (y)

ln (10 e^{- \frac{2 10}{5} x})

ln (\frac{1}{x + 2})

- lo g_{10} (7 \cdot 1 0^{- 5})

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

What is expand log_{5}(x^3y^2) ?
The solution to expand log_{5}(x^3y^2) is 3log_{5}(x)+2log_{5}(y)