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

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

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simplify ln((xsqrt(x+1))/(x^2+1))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x x + 1) = ln (x) + ln (x + 1)

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

lo g_{10} (3 b)

lo g_{7} (x) - lo g_{7} (x^{6})

4 ln (x) - \frac{1}{9} ln (y)

lo g_{3} (2 x)

2 lo g_{4} (y) + 5 lo g_{4} (x) - \frac{1}{2} lo g_{4} (z)

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