What is ln(x^2sqrt(4-x^2)) ?

The solution to ln(x^2sqrt(4-x^2)) is 2ln(x)+ln(sqrt(4-x^2))

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simplify ln(x^2sqrt(4-x^2))

simplify

ln (x^{2} 4 - x^{2})

2 ln (x) + ln (4 - x^{2})

Solution steps

ln (x^{2} 4 - x^{2})

Apply log rule:

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

ln (x^{2} 4 - x^{2}) = ln (x^{2}) + ln (4 - x^{2})

= ln (x^{2}) + ln (- x^{2} + 4)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 2 ln (x) + ln (4 - x^{2})

10 (lo g_{10} (0.001) - lo g_{10} (x) + 12)

ln (\frac{140000}{( 140000 - 2100 x )})

2 ln ∣ x ∣ - ln ∣ x - 3 ∣

2 ln^{x} (+ \frac{1}{2} ln (x - 1) - 3 ln (x + 7))

\frac{1}{3} ln (\frac{9 + 3 17}{2})

What is ln(x^2sqrt(4-x^2)) ?
The solution to ln(x^2sqrt(4-x^2)) is 2ln(x)+ln(sqrt(4-x^2))