What is expand ln(sqrt((x-1)/x)) ?

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

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expand ln(sqrt((x-1)/x))

expand

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

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

Solution steps

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

Rewrite as

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

\frac{( 2 h - a ) ( 2 h - 3 a )}{2}

\frac{3 ( x ^{2} + 1 ) ^{\frac{5}{2}} - 5 ( x ^{2} + 1 ) ^{\frac{3}{2}}}{15}

(3 - e^{2 x^{2} + x})^{4}

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

\frac{1}{81} (2 + s)^{4}

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