What is expand log_{10}(sqrt((2x)/y)) ?

The solution to expand log_{10}(sqrt((2x)/y)) is 1/2 log_{10}((2x)/y)

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expand log_{10}(sqrt((2x)/y))

expand

lo g_{10} (\frac{2 x}{y})

\frac{1}{2} lo g_{10} (\frac{2 x}{y})

Solution steps

lo g_{10} (\frac{2 x}{y})

Rewrite as

= lo g_{10} ((\frac{2 x}{y})^{\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_{10} (\frac{2 x}{y})

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What is expand log_{10}(sqrt((2x)/y)) ?
The solution to expand log_{10}(sqrt((2x)/y)) is 1/2 log_{10}((2x)/y)