What is expand log_{3}(sqrt(x/(y^3z^2))) ?

The solution to expand log_{3}(sqrt(x/(y^3z^2))) is 1/2 log_{3}(x/(y^3z^2))

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expand log_{3}(sqrt(x/(y^3z^2)))

expand

lo g_{3} (\frac{x}{y ^{3} z ^{2}})

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

Solution steps

lo g_{3} (\frac{x}{y ^{3} z ^{2}})

Rewrite as

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

Apply log rule

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

assuming

x \geq 0

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

\frac{3 ( 7 + 35 x )}{10}

\frac{( 4 + 3 x ) ^{2}}{x}

(x + 4) (x + 4 + 2 i) (x - 4 - 2 i)

\frac{3 ( 2 - x ) ^{2}}{2}

\frac{4 ( a - 1 )}{4 a - 3}

What is expand log_{3}(sqrt(x/(y^3z^2))) ?
The solution to expand log_{3}(sqrt(x/(y^3z^2))) is 1/2 log_{3}(x/(y^3z^2))