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

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

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

expand

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

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

Solution steps

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

Rewrite as

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

(x - 5) (x + 5)

x^{2} (1 + 1 - x^{2})

\frac{( 3 x ^{4} )}{( 8 x ^{5} - 3 ) ^{4}}

2 x (1 + 2 ln (x))

(x - 5) (x - \frac{7}{3})

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