What is expand log_{n}(sqrt((mn)/(n+1))) ?

The solution to expand log_{n}(sqrt((mn)/(n+1))) is 1/2 log_{n}((mn)/(n+1))

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expand log_{n}(sqrt((mn)/(n+1)))

expand

lo g_{n} (\frac{mn}{n + 1})

\frac{1}{2} lo g_{n} (\frac{mn}{n + 1})

Solution steps

lo g_{n} (\frac{mn}{n + 1})

Rewrite as

= lo g_{n} ((\frac{mn}{n + 1})^{\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_{n} (\frac{mn}{n + 1})

\frac{1}{( e ^{2 A T} - 1 ) ( e ^{- 2 A T} - 1 )}

\frac{( 1 + x ) ^{2}}{x ( 1 + x ^{2} )}

\frac{y ( 25 y - 32 ) ^{2}}{1012}

(y cos (x) + 2 x e^{y}) + (sin (x) + x^{2} e^{y - 1}) y^{'} (x)

\frac{a ^{2} + b ^{2}}{( 3 ) ( a ^{2} + 4 + b ^{2} )}

What is expand log_{n}(sqrt((mn)/(n+1))) ?
The solution to expand log_{n}(sqrt((mn)/(n+1))) is 1/2 log_{n}((mn)/(n+1))