What is expand log_{b}(sqrt(57/74)) ?

The solution to expand log_{b}(sqrt(57/74)) is 1/2 log_{b}(57/74)

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expand log_{b}(sqrt(57/74))

expand

lo g_{b} (\frac{57}{74})

\frac{1}{2} lo g_{b} (\frac{57}{74})

Solution steps

lo g_{b} (\frac{57}{74})

Rewrite as

= lo g_{b} ((\frac{57}{74})^{\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_{b} (\frac{57}{74})

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(x^{3} - \frac{1}{2 x})^{12}

What is expand log_{b}(sqrt(57/74)) ?
The solution to expand log_{b}(sqrt(57/74)) is 1/2 log_{b}(57/74)