What is expand ln(sqrt((6x)/(x-6))) ?

The solution to expand ln(sqrt((6x)/(x-6))) is 1/2 ln((6x)/(x-6))

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expand ln(sqrt((6x)/(x-6)))

expand

ln (\frac{6 x}{x - 6})

\frac{1}{2} ln (\frac{6 x}{x - 6})

Solution steps

ln (\frac{6 x}{x - 6})

Rewrite as

= ln ((\frac{6 x}{x - 6})^{\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{6 x}{x - 6})

(\frac{( 1 + 5 )}{2})^{2}

\frac{3 x ^{3} - 4 x + 5}{( x - 1 ) ( x ^{2} + 2 x + 1 )}

\frac{2 x ^{2} + x + 8}{( x ^{2} + 4 ) ^{2}}

(1 + y^{2}) d x

\frac{( 3 - 5 + x ) ( 1 + 5 - x )}{x - 4}

What is expand ln(sqrt((6x)/(x-6))) ?
The solution to expand ln(sqrt((6x)/(x-6))) is 1/2 ln((6x)/(x-6))