What is expand log_{10}(sqrt((a-b)/(a+b))) ?

The solution to expand log_{10}(sqrt((a-b)/(a+b))) is 1/2 log_{10}((a-b)/(a+b))

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expand log_{10}(sqrt((a-b)/(a+b)))

expand

lo g_{10} (\frac{a - b}{a + b})

\frac{1}{2} lo g_{10} (\frac{a - b}{a + b})

Solution steps

lo g_{10} (\frac{a - b}{a + b})

Rewrite as

= lo g_{10} ((\frac{a - b}{a + b})^{\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{a - b}{a + b})

- \frac{0.0951}{( x - 1 ) ( x - 0.9048 )}

\frac{( x - 6 ) ^{2}}{x + 6}

(e^{2 x^{3} + 6 x^{2} - 48 x}) \cdot (6 x^{2} + 12 x - 48)

x^{4} (1 - \frac{2}{x - 1})

What is expand log_{10}(sqrt((a-b)/(a+b))) ?
The solution to expand log_{10}(sqrt((a-b)/(a+b))) is 1/2 log_{10}((a-b)/(a+b))