What is expand ln(sqrt((x-73)/x)) ?

The solution to expand ln(sqrt((x-73)/x)) is 1/2 ln((x-73)/x)

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expand ln(sqrt((x-73)/x))

expand

ln (\frac{x - 73}{x})

\frac{1}{2} ln (\frac{x - 73}{x})

Solution steps

ln (\frac{x - 73}{x})

Rewrite as

= ln ((\frac{x - 73}{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 - 73}{x})

\frac{( n ) ( n + 1 ) ( 2 n + 1 )}{6}

(x + 3 + 6) (x + 3 - 6)

\frac{12 x ^{2} - 27}{3}

lo g_{\frac{x ( x + 7 )}{( x + 3 ) ^{4}}} (x)

3 (4 x ln (x) + 2 x)

What is expand ln(sqrt((x-73)/x)) ?
The solution to expand ln(sqrt((x-73)/x)) is 1/2 ln((x-73)/x)