What is expand ln(sqrt((x-67)/x)) ?

The solution to expand ln(sqrt((x-67)/x)) is 1/2 ln((x-67)/x)

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expand ln(sqrt((x-67)/x))

expand

ln (\frac{x - 67}{x})

\frac{1}{2} ln (\frac{x - 67}{x})

Solution steps

ln (\frac{x - 67}{x})

Rewrite as

= ln ((\frac{x - 67}{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 - 67}{x})

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

e^{x} (e^{- x} + e^{x})

e^{x} (x^{3} - 1)

(2 x + 2)^{2}

\frac{( x ^{2} + 7 x - 1 ) ( x - 7 )}{( x - 2 ) ( x ^{2} + 9 x )}

What is expand ln(sqrt((x-67)/x)) ?
The solution to expand ln(sqrt((x-67)/x)) is 1/2 ln((x-67)/x)