What is expand 2log_{2}(x)+8log_{2}(y) ?

The solution to expand 2log_{2}(x)+8log_{2}(y) is log_{2}(x^2y^8)

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expand 2log_{2}(x)+8log_{2}(y)

expand

2 lo g_{2} (x) + 8 lo g_{2} (y)

lo g_{2} (x^{2} y^{8})

Solution steps

2 lo g_{2} (x) + 8 lo g_{2} (y)

Apply log rule:

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

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

= lo g_{2} (x^{2}) + 8 lo g_{2} (y)

Apply log rule:

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

8 lo g_{2} (y) = lo g_{2} (y^{8})

= lo g_{2} (x^{2}) + lo g_{2} (y^{8})

Apply log rule:

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

lo g_{2} (x^{2}) + lo g_{2} (y^{8}) = lo g_{2} (x^{2} y^{8})

= lo g_{2} (x^{2} y^{8})

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What is expand 2log_{2}(x)+8log_{2}(y) ?
The solution to expand 2log_{2}(x)+8log_{2}(y) is log_{2}(x^2y^8)