What is expand ln(sqrt((2x)/(x-2))) ?

The solution to expand ln(sqrt((2x)/(x-2))) is 1/2 ln((2x)/(x-2))

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expand ln(sqrt((2x)/(x-2)))

expand

ln (\frac{2 x}{x - 2})

\frac{1}{2} ln (\frac{2 x}{x - 2})

Solution steps

ln (\frac{2 x}{x - 2})

Rewrite as

= ln ((\frac{2 x}{x - 2})^{\frac{1}{2}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{2} ln (\frac{2 x}{x - 2})

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

P (6, 5) y Q (2, - 3)

F (3, - \frac{3}{4})

\frac{( x ^{2} - 2 x + 3 )}{( x - 3 ) ( x ^{2} + 9 )}

\frac{e ^{- s} ( 1 - s )}{s ^{2}}

What is expand ln(sqrt((2x)/(x-2))) ?
The solution to expand ln(sqrt((2x)/(x-2))) is 1/2 ln((2x)/(x-2))