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

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

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simplify ln(x)-ln(sqrt(x^2+1))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

\frac{x}{x ^{2} + 1} : \frac{x x ^{2} + 1}{x ^{2} + 1}

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

ln (θ^{- 1} e^{- \frac{x}{θ}})

- 18 ln (3.5) + 18 ln (2)

lo g_{e} (\frac{5 y}{x ^{3}})

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

5 ln (5) - 4 ln (4) - 3 ln (3)

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