What is expand ln(sqrt(x^2(x+2))) ?

The solution to expand ln(sqrt(x^2(x+2))) is ln(x)+1/2 ln(x+2)

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expand ln(sqrt(x^2(x+2)))

expand

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

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

Solution steps

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

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

= ln (x x + 2)

Apply log rule:

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

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

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

Simplify

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

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

(2 x - 5) (2 x + 5)

\frac{2}{( s ^{2} - 2 s + 2 ) ^{2}}

\frac{x ( x + 1 ) ( 2 x + 1 )}{6}

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

(x - 2 + 3) (x - 2 - 3)

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