What is expand ln(sqrt(7*x^9y^2)) ?

The solution to expand ln(sqrt(7*x^9y^2)) is ln(y)+9/2 ln(x)+1/2 ln(7)

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expand ln(sqrt(7*x^9y^2))

expand

ln (7 \cdot x^{9} y^{2})

ln (y) + \frac{9}{2} ln (x) + \frac{1}{2} ln (7)

Solution steps

ln (7 x^{9} y^{2})

7 x^{9} y^{2} = 7 x^{4} y x

= ln (7 x^{4} y x)

Apply log rule:

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

ln (7 x^{4} x y) = ln (x^{4} x y) + ln (7)

= ln (x^{4} y x) + ln (7)

Simplify

ln (7) : \frac{1}{2} ln (7)

= ln (x^{4} y x) + \frac{1}{2} ln (7)

ln (x^{4} x y) = ln (y) + \frac{9}{2} ln (x)

= ln (y) + \frac{9}{2} ln (x) + \frac{1}{2} ln (7)

(e^{3 t} - 1)^{2}

x (x + 1) d x

e^{a t} (H (t - 1) - H (t - 2))

(y e^{x y} + 3 x^{2}) d x + (x e^{x y} - cos (y)) d y

f (x) = (e^{x} + 2 x)^{4}

What is expand ln(sqrt(7*x^9y^2)) ?
The solution to expand ln(sqrt(7*x^9y^2)) is ln(y)+9/2 ln(x)+1/2 ln(7)