What is expand ln((x^3sqrt(x^2+1))/((x+1)^2)) ?

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

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expand ln((x^3sqrt(x^2+1))/((x+1)^2))

expand

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

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

Solution steps

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

Apply log rule:

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

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

= ln (x^{3} x^{2} + 1) - ln ((x + 1)^{2})

Apply log rule:

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

ln ((x + 1)^{2}) = 2 ln (x + 1)

= ln (x^{3} x^{2} + 1) - 2 ln (x + 1)

Apply log rule:

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

ln (x^{3} x^{2} + 1) = ln (x^{3}) + ln (x^{2} + 1)

= ln (x^{3}) + ln (x^{2} + 1) - 2 ln (x + 1)

Apply log rule:

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

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

= 3 ln (x) + ln (x^{2} + 1) - 2 ln (x + 1)

ln (\frac{20}{30})

- lo g_{10} (3 \cdot 1 0^{- 7})

ln (\frac{2 t}{θ} e^{\frac{- t ^{2}}{θ}})

150 ln (\frac{350}{400 - x})

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