What is 12log_{10}(x)+5log_{10}(y) ?

The solution to 12log_{10}(x)+5log_{10}(y) is log_{10}(x^{12}y^5)

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simplify 12log_{10}(x)+5log_{10}(y)

simplify

12 lo g_{10} (x) + 5 lo g_{10} (y)

lo g_{10} (x^{12} y^{5})

Solution steps

12 lo g_{10} (x) + 5 lo g_{10} (y)

Apply log rule:

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

12 lo g_{10} (x) = lo g_{10} (x^{12})

= lo g_{10} (x^{12}) + 5 lo g_{10} (y)

Apply log rule:

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

5 lo g_{10} (y) = lo g_{10} (y^{5})

= lo g_{10} (x^{12}) + lo g_{10} (y^{5})

Apply log rule:

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

lo g_{10} (x^{12}) + lo g_{10} (y^{5}) = lo g_{10} (x^{12} y^{5})

= lo g_{10} (x^{12} y^{5})

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What is 12log_{10}(x)+5log_{10}(y) ?
The solution to 12log_{10}(x)+5log_{10}(y) is log_{10}(x^{12}y^5)