What is 6log_{3}(x)+12log_{3}(y) ?

The solution to 6log_{3}(x)+12log_{3}(y) is log_{3}(x^6y^{12})

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simplify 6log_{3}(x)+12log_{3}(y)

simplify

6 lo g_{3} (x) + 12 lo g_{3} (y)

lo g_{3} (x^{6} y^{12})

Solution steps

6 lo g_{3} (x) + 12 lo g_{3} (y)

Apply log rule:

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

6 lo g_{3} (x) = lo g_{3} (x^{6})

= lo g_{3} (x^{6}) + 12 lo g_{3} (y)

Apply log rule:

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

12 lo g_{3} (y) = lo g_{3} (y^{12})

= lo g_{3} (x^{6}) + lo g_{3} (y^{12})

Apply log rule:

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

lo g_{3} (x^{6}) + lo g_{3} (y^{12}) = lo g_{3} (x^{6} y^{12})

= lo g_{3} (x^{6} y^{12})

ln (\frac{1}{1 + 2})

lo g_{2} (\frac{a}{b})

6 lo g_{10} (3) - 4 lo g_{10} (2)

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

What is 6log_{3}(x)+12log_{3}(y) ?
The solution to 6log_{3}(x)+12log_{3}(y) is log_{3}(x^6y^{12})