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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{6} (x - 7) + lo g_{6} (x + 7)

lo g_{9} (7) + lo g_{9} (4)

- 20 lo g_{4} (x) - 80 lo g_{4} (y)

\frac{1}{3} lo g_{3} (8) - lo g_{3} (10) + 4 lo g_{3} (2)

lo g_{10} (2.5) + 0.4 lo g_{10} (x)

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