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write the expression as a sinle logarithm. express powers as factors.

In (x/x-1)+In(x+1/x)-In(x^2-1)

Please show work.

  • math -

    You MUST put brackets for the denominators to avoid ambiguity

    I am sure you mean

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

    = lnx - ln(x+1) + (ln(x+1) - lnx - ln( (x+1)(x-1)
    = lnx - ln(x+1) + ln(x+1) + lnx - ln(x+1) - ln(x-1)
    = - 2ln(x+1)


    ln [ (x/(x-1) ((x+1)/x) / ((x+1)x-1))
    = ln (1/(x-1)^2)
    = ln1 - ln(x-1)^2
    = 0 - 2ln(x-1)
    = -2ln(x-1)

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