What is expand log_{10}(sqrt((xy^2)/(2m))) ?

The solution to expand log_{10}(sqrt((xy^2)/(2m))) is 1/2 log_{10}((xy^2)/(2m))

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expand log_{10}(sqrt((xy^2)/(2m)))

expand

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

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

Solution steps

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

Rewrite as

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

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e^{2 x} x (- 3 e^{x} x - 7 e^{x})

What is expand log_{10}(sqrt((xy^2)/(2m))) ?
The solution to expand log_{10}(sqrt((xy^2)/(2m))) is 1/2 log_{10}((xy^2)/(2m))