Asked by Alley
Write the expression as a single log. Express powers as factors
ln(x/x-5) + ln(x+5/x) - ln(x^2-25)
ln(x/x-5) + ln(x+5/x) - ln(x^2-25)
Answers
Answered by
Reiny
I am sure you meant to type
ln( x/(x-5) ) + ln( (x+5)/x ) - ln(x^2 - 25)
= lnx - ln(x-5) + ln(x+5) - lnx - (ln(x+5) + ln(x-5)
= -ln(x-5) + ln(x+5) - ln(x+5) - ln(x-5)
= -2ln(x-5)
ln( x/(x-5) ) + ln( (x+5)/x ) - ln(x^2 - 25)
= lnx - ln(x-5) + ln(x+5) - lnx - (ln(x+5) + ln(x-5)
= -ln(x-5) + ln(x+5) - ln(x+5) - ln(x-5)
= -2ln(x-5)
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