Question

write the expression as a simple logarithm. express powers.

In(x/x-5)+In(x+5/x)-In(x^2-25)

Answer 1

Assuming you meant:

In(x/(x-5))+In((x+5)/x)-In(x^2-25)
= lnx - ln(x-5) + ln(x+5) - lnx - ( ln(x+5) + ln(x-5) )
= lnx - ln(x-5) + ln(x+5) - lnx - ln(x+5) - ln(x-5)
= -2ln(x-5)
or -ln(x-5)^2 or ln(x-5)^-2