What is expand log_{3}(\sqrt[3]{(m^2)/(xz^2)}) ?

The solution to expand log_{3}(\sqrt[3]{(m^2)/(xz^2)}) is 1/3 (2log_{3}(m)-log_{3}(xz^2))

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expand log_{3}(\sqrt[3]{(m^2)/(xz^2)})

expand

\frac{1}{3} (2 lo g_{3} (m) - lo g_{3} (x z^{2}))

Solution steps

Rewrite as

= lo g_{3} ((\frac{m ^{2}}{x z ^{2}})^{\frac{1}{3}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{3} lo g_{3} (\frac{m ^{2}}{x z ^{2}})

Simplify

lo g_{3} (\frac{m ^{2}}{x z ^{2}}) : 2 lo g_{3} (m) - lo g_{3} (x z^{2})

= \frac{1}{3} (2 lo g_{3} (m) - lo g_{3} (x z^{2}))

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

= \frac{1}{3} (2 lo g_{3} (m) - (lo g_{3} (x) + 2 lo g_{3} (z)))

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

= \frac{1}{3} (2 lo g_{3} (m) - lo g_{3} (x z^{2}))

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

= \frac{1}{3} (2 lo g_{3} (m) - (lo g_{3} (x) + 2 lo g_{3} (z)))

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

= \frac{1}{3} (2 lo g_{3} (m) - lo g_{3} (x z^{2}))

(- 10 + 5) x

\frac{2 x + 15 + 2}{2 ( x - 3 ) ( x + 10 )}

(T - a) (T - b) (T - c) (T - d) (T - e)

p a r t s [(- 30 x^{2} - 3 x) e^{- 5 x}] d x

(4 \cdot x \cdot y + 4 y^{2} + 1) d x + (x^{2} + 2 \cdot x \cdot y) d y

What is expand log_{3}(\sqrt[3]{(m^2)/(xz^2)}) ?
The solution to expand log_{3}(\sqrt[3]{(m^2)/(xz^2)}) is 1/3 (2log_{3}(m)-log_{3}(xz^2))