# math

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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)

• 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)

then
= 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)

or

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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