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

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

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simplify 3log_{2}(x)+5log_{2}(y)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{2} (x) = lo g_{2} (x^{3})

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

lo g_{5} (x^{3} y^{6})

lo g_{b} (z^{7} x)

lo g_{10} (c) - 5 lo g_{10} (k)

ln (\frac{9}{2 x ^{2} y})

lo g_{10} (x) + 2 lo g_{10} (y) - 3 lo g_{10} (z)

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