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

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

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

simplify

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

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

Solution steps

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

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

Apply log rule:

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

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

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

- lo g_{10} (9.2 \cdot 1 0^{- 2})

ln (2 x) + ln (y^{2})

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ln (x - 2^{\frac{3}{2}} - 2) - ln (x + 2^{\frac{3}{2}} - 2)

- \frac{1}{3} ln (\frac{1}{10000000000000})

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