What is expand ln(sqrt(4x^3y)) ?

The solution to expand ln(sqrt(4x^3y)) is ln(2x)+1/2 ln(xy)

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expand ln(sqrt(4x^3y))

expand

ln (4 x^{3} y)

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

Solution steps

ln (4 x^{3} y)

4 x^{3} y = 2 x x y

= ln (2 x x y)

Apply log rule:

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

ln (2 x x y) = ln (2 x) + ln (x y)

= ln (2 x) + ln (x y)

Simplify

ln (x y) : \frac{1}{2} ln (x y)

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

20 lo g_{10} (x z)

(2 x - 1) x

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

(x + 3 y) (x - 3 y)

\frac{x ^{4} ( x - 5 )}{100}

What is expand ln(sqrt(4x^3y)) ?
The solution to expand ln(sqrt(4x^3y)) is ln(2x)+1/2 ln(xy)