What is 24log_{2}(x)+6log_{2}(y) ?

The solution to 24log_{2}(x)+6log_{2}(y) is log_{2}(x^{24}y^6)

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simplify 24log_{2}(x)+6log_{2}(y)

simplify

24 lo g_{2} (x) + 6 lo g_{2} (y)

lo g_{2} (x^{24} y^{6})

Solution steps

24 lo g_{2} (x) + 6 lo g_{2} (y)

Apply log rule:

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

24 lo g_{2} (x) = lo g_{2} (x^{24})

= lo g_{2} (x^{24}) + 6 lo g_{2} (y)

Apply log rule:

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

6 lo g_{2} (y) = lo g_{2} (y^{6})

= lo g_{2} (x^{24}) + lo g_{2} (y^{6})

Apply log rule:

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

lo g_{2} (x^{24}) + lo g_{2} (y^{6}) = lo g_{2} (x^{24} y^{6})

= lo g_{2} (x^{24} y^{6})

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What is 24log_{2}(x)+6log_{2}(y) ?
The solution to 24log_{2}(x)+6log_{2}(y) is log_{2}(x^{24}y^6)