What is expand ln((x^2sqrt(x^2+3))/((x+3)^4)) ?

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

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expand ln((x^2sqrt(x^2+3))/((x+3)^4))

expand

ln (\frac{x ^{2} x ^{2} + 3}{( x + 3 ) ^{4}})

2 ln (x) + ln (x^{2} + 3) - 4 ln (x + 3)

Solution steps

ln (\frac{x ^{2} x ^{2} + 3}{( x + 3 ) ^{4}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{x ^{2} x ^{2} + 3}{( x + 3 ) ^{4}}) = ln (x^{2} x^{2} + 3) - ln ((x + 3)^{4})

= ln (x^{2} x^{2} + 3) - ln ((x + 3)^{4})

Apply log rule:

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

ln ((x + 3)^{4}) = 4 ln (x + 3)

= ln (x^{2} x^{2} + 3) - 4 ln (x + 3)

Apply log rule:

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

ln (x^{2} x^{2} + 3) = ln (x^{2}) + ln (x^{2} + 3)

= ln (x^{2}) + ln (x^{2} + 3) - 4 ln (x + 3)

Apply log rule:

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

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

= 2 ln (x) + ln (x^{2} + 3) - 4 ln (x + 3)

6 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

ln (v - 1) - ln (v)

ln (- \frac{1}{6} (x^{2} - 6 x + 5))

- lo g_{10} (4.4 \cdot 1 0^{- 4}) - 14

ln (0.9 - 0.5) - ln (x)

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