What is 2*log_{3}(sqrt(x))+3*log_{3}(2y) ?

The solution to 2*log_{3}(sqrt(x))+3*log_{3}(2y) is log_{3}(8xy^3)

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simplify 2log_{3}(sqrt(x))+3log_{3}(2y)

simplify

2 \cdot lo g_{3} (x) + 3 \cdot lo g_{3} (2 y)

lo g_{3} (8 x y^{3})

Solution steps

2 lo g_{3} (x) + 3 lo g_{3} (2 y)

2 lo g_{3} (x) = lo g_{3} ((x)^{2})

3 lo g_{3} (2 y) = lo g_{3} ((2 y)^{3})

= lo g_{3} ((x)^{2}) + lo g_{3} ((2 y)^{3})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{3} ((x)^{2}) + lo g_{3} ((2 y)^{3}) = lo g_{3} ((x)^{2} (2 y)^{3})

= lo g_{3} ((x)^{2} (2 y)^{3})

Simplify

(x)^{2} (2 y)^{3} : x \cdot 8 y^{3}

= lo g_{3} (x \cdot 8 y^{3})

= lo g_{3} (8 x y^{3})

f (x) = ln (x^{9}) - ln (x)

ln (\frac{1}{e})

lo g_{3} (\frac{x ^{5} y}{w ^{3} z})

lo g_{10} (\frac{1}{x})

lo g_{10} (61 v w)

What is 2*log_{3}(sqrt(x))+3*log_{3}(2y) ?
The solution to 2*log_{3}(sqrt(x))+3*log_{3}(2y) is log_{3}(8xy^3)