What is expand ln(sqrt(6x^9y^5)) ?

The solution to expand ln(sqrt(6x^9y^5)) is 2ln(x^2y)+1/2 ln(xy)+1/2 ln(6)

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expand ln(sqrt(6x^9y^5))

expand

ln (6 x^{9} y^{5})

2 ln (x^{2} y) + \frac{1}{2} ln (x y) + \frac{1}{2} ln (6)

Solution steps

ln (6 x^{9} y^{5})

6 x^{9} y^{5} = 6 x^{4} y^{2} x y

= ln (6 x^{4} y^{2} x y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (6 x^{4} x y y^{2}) = ln (x^{4} x y y^{2}) + ln (6)

= ln (x^{4} y^{2} x y) + ln (6)

Simplify

ln (6) : \frac{1}{2} ln (6)

= ln (x^{4} y^{2} x y) + \frac{1}{2} ln (6)

ln (x^{4} x y y^{2}) = 2 (ln (y) + 2 ln (x)) + \frac{1}{2} ln (x y)

= 2 (2 ln (x) + ln (y)) + \frac{1}{2} ln (x y) + \frac{1}{2} ln (6)

ln (y) + 2 ln (x) = ln (y x^{2})

= 2 ln (x^{2} y) + \frac{1}{2} ln (x y) + \frac{1}{2} ln (6)

Simplify

ln (x^{2} y) : 2 ln (x) + ln (y)

= 2 (2 ln (x) + ln (y)) + \frac{1}{2} ln (x y) + \frac{1}{2} ln (6)

ln (y) + 2 ln (x) = ln (y x^{2})

= 2 ln (x^{2} y) + \frac{1}{2} ln (x y) + \frac{1}{2} ln (6)

\frac{2 ( 9 - 3 )}{3}

(x cos (x) - sin (x)) (- cos (x))

lo g_{4} (4) (x - 3)

11 (8 r + 3) - 2 (- 9 = 6 r)

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

What is expand ln(sqrt(6x^9y^5)) ?
The solution to expand ln(sqrt(6x^9y^5)) is 2ln(x^2y)+1/2 ln(xy)+1/2 ln(6)