What is expand log_{5}(x^4y^3) ?

The solution to expand log_{5}(x^4y^3) is 4log_{5}(x)+3log_{5}(y)

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expand log_{5}(x^4y^3)

expand

lo g_{5} (x^{4} y^{3})

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

Solution steps

lo g_{5} (x^{4} y^{3})

Apply log rule:

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

lo g_{5} (x^{4} y^{3}) = lo g_{5} (x^{4}) + lo g_{5} (y^{3})

= lo g_{5} (x^{4}) + lo g_{5} (y^{3})

Apply log rule:

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

lo g_{5} (x^{4}) = 4 lo g_{5} (x)

= 4 lo g_{5} (x) + lo g_{5} (y^{3})

Apply log rule:

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

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

= 4 lo g_{5} (x) + 3 lo g_{5} (y)

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

\frac{1}{2} lo g_{49} (3)

2 lo g_{e} (\frac{2}{3})

ln (\frac{93079.22}{1000})

ln (x^{2} (y - 2)^{3})

What is expand log_{5}(x^4y^3) ?
The solution to expand log_{5}(x^4y^3) is 4log_{5}(x)+3log_{5}(y)