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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

2.69 - \frac{0.02569}{2} ln (\frac{0. 4 ^{3}}{2 ^{2}})

\frac{1}{3} ln (5)

- (- \frac{1}{3} ln (5 + 1) + \frac{1}{3} ln (5 - 2))

ln (\frac{y}{2})

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

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