What is expand ln(sqrt((9x)/(x-9))) ?

The solution to expand ln(sqrt((9x)/(x-9))) is ln(3)+1/2 ln(x)-1/2 ln(x-9)

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expand ln(sqrt((9x)/(x-9)))

expand

ln (\frac{9 x}{x - 9})

ln (3) + \frac{1}{2} ln (x) - \frac{1}{2} ln (x - 9)

Solution steps

ln (\frac{9 x}{x - 9})

\frac{9 x}{x - 9} = \frac{3 x}{x - 9}

= ln (\frac{3 x}{x - 9})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{3 x}{x - 9}) = ln (3 x) - ln (x - 9)

= ln (3 x) - ln (x - 9)

Simplify

ln (x - 9) : \frac{1}{2} ln (x - 9)

ln (3 x) = ln (3) + \frac{1}{2} ln (x)

= ln (3) + \frac{1}{2} ln (x) - \frac{1}{2} ln (x - 9)

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

\frac{( k + 1 ) ( k + 2 ) ( 2 k + 9 )}{6}

lo g_{4} (3 x^{2} y^{4})

- ln 1 + cos^{2} (7.5)

\frac{8 x}{( x + 2 ) ( x - 2 )}

What is expand ln(sqrt((9x)/(x-9))) ?
The solution to expand ln(sqrt((9x)/(x-9))) is ln(3)+1/2 ln(x)-1/2 ln(x-9)