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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

Apply log rule:

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

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

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

5 lo g_{4} (x) - lo g_{4} (6)

ln (\frac{2 \cdot 1 0 ^{6}}{1 0 ^{6}})

- lo g_{10} (3.9 \cdot 1 0^{- 8})

- lo g_{10} (6 \cdot 1 0^{- 5})

3 lo g_{5} (x) - 2 lo g_{5} (y)

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