What is ln((x^9sqrt(x^2+1))/((x+1)^9)) ?

The solution to ln((x^9sqrt(x^2+1))/((x+1)^9)) is 9ln(x)+ln(sqrt(x^2+1))-9ln(x+1)

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simplify ln((x^9sqrt(x^2+1))/((x+1)^9))

simplify

ln (\frac{x ^{9} x ^{2} + 1}{( x + 1 ) ^{9}})

9 ln (x) + ln (x^{2} + 1) - 9 ln (x + 1)

Solution steps

ln (\frac{x ^{9} x ^{2} + 1}{( x + 1 ) ^{9}})

Apply log rule:

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

ln (\frac{x ^{9} x ^{2} + 1}{( x + 1 ) ^{9}}) = ln (x^{9} x^{2} + 1) - ln ((x + 1)^{9})

= ln (x^{9} x^{2} + 1) - ln ((x + 1)^{9})

Apply log rule:

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

ln ((x + 1)^{9}) = 9 ln (x + 1)

= ln (x^{9} x^{2} + 1) - 9 ln (x + 1)

Apply log rule:

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

ln (x^{9} x^{2} + 1) = ln (x^{9}) + ln (x^{2} + 1)

= ln (x^{9}) + ln (x^{2} + 1) - 9 ln (x + 1)

Apply log rule:

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

ln (x^{9}) = 9 ln (x)

= 9 ln (x) + ln (x^{2} + 1) - 9 ln (x + 1)

lo g_{b} (12) - lo g_{b} (6)

ln (x x)

5.14 + lo g_{10} (\frac{0.05}{0.4 - 0.05})

lo g_{10} (\frac{11 x}{2})

What is ln((x^9sqrt(x^2+1))/((x+1)^9)) ?
The solution to ln((x^9sqrt(x^2+1))/((x+1)^9)) is 9ln(x)+ln(sqrt(x^2+1))-9ln(x+1)