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

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

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expand log_{3}(sqrt(x/z))

expand

lo g_{3} (\frac{x}{z})

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

Solution steps

lo g_{3} (\frac{x}{z})

Rewrite as

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

\frac{s ( s ^{2} + 6 s + 4 )}{( s - 3 ) ( s + 2 ) ( s + 6 )}

\frac{2 ( 1 - 6 )}{5}

3 (10 - 1)

(2 - x) x

z (- \frac{2}{3} z + 2)^{2}

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