What is expand log_{3}(\sqrt[4]{x^{12}y}) ?

The solution to expand log_{3}(\sqrt[4]{x^{12}y}) is 3log_{3}(x)+1/4 log_{3}(y)

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expand log_{3}(\sqrt[4]{x^{12}y})

expand

3 lo g_{3} (x) + \frac{1}{4} lo g_{3} (y)

Solution steps

Apply log rule:

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

Apply log rule:

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

Apply log rule:

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

Simplify

= lo g_{3} (x^{3}) + \frac{1}{4} lo g_{3} (y)

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= 3 lo g_{3} (x) + \frac{1}{4} lo g_{3} (y)

\frac{- 2 t ^{5} - 2 t}{( t ^{4} - 1 ) ^{2} ( t ^{2} - 1 )}

A (- 1, 0) B (\frac{3}{2}, - \frac{1}{2})

4 sin (2 (π + θ))

d x d (3 x^{2} - 1)

\frac{12}{8}

What is expand log_{3}(\sqrt[4]{x^{12}y}) ?
The solution to expand log_{3}(\sqrt[4]{x^{12}y}) is 3log_{3}(x)+1/4 log_{3}(y)