Asked by ladybug
write the expression as a simple logarithm. express powers.
In(x/x-5)+In(x+5/x)-In(x^2-25)
In(x/x-5)+In(x+5/x)-In(x^2-25)
Answers
Answered by
Reiny
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
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
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