What is log_{3}((asqrt(b))/(12)) ?

The solution to log_{3}((asqrt(b))/(12)) is log_{3}(a)+log_{3}(sqrt(b))-1-2log_{3}(2)

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simplify log_{3}((asqrt(b))/(12))

simplify

lo g_{3} (\frac{a b}{12})

lo g_{3} (a) + lo g_{3} (b) - 1 - 2 lo g_{3} (2)

Solution steps

lo g_{3} (\frac{a b}{12})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{3} (\frac{a b}{12}) = lo g_{3} (a b) - lo g_{3} (12)

= lo g_{3} (a b) - lo g_{3} (12)

lo g_{3} (a b) = lo g_{3} (a) + lo g_{3} (b)

lo g_{3} (12) = 1 + 2 lo g_{3} (2)

= lo g_{3} (a) + lo g_{3} (b) - (1 + 2 lo g_{3} (2))

Apply the distributive law:

- (a + b) = - a - b

- (1 + 2 lo g_{3} (2)) = - 1 - 2 lo g_{3} (2)

= lo g_{3} (a) + lo g_{3} (b) - 1 - 2 lo g_{3} (2)

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What is log_{3}((asqrt(b))/(12)) ?
The solution to log_{3}((asqrt(b))/(12)) is log_{3}(a)+log_{3}(sqrt(b))-1-2log_{3}(2)