Thread: fun with natural logs....

ok so we have the problem...

ln N - ln(N-2000)= t + C

so i tried to say that ln a = ln B = ln (a/B)

so i got ln(N/N-2000)= t + c

so then i raised both sides to e and got

N/N-2000 = e^(t+c)

my final answer was -2000e^(t+c)/(1-e^(t+c))

my book got the same thing except their answer was positive, i dont see how this could be possible? can someone tell me where i went wrong

Originally Posted by slapmaxwell1

ok so we have the problem...

ln N - ln(N-2000)= t + C

so i tried to say that ln a = ln B = ln (a/B)

so i got ln(N/N-2000)= t + C

so then i raised both sides to e and got

N/N-2000 = e^(t+C)

my final answer was -2000e^(t+c)/(1-e^(t+c))

my book got the same thing except their answer was positive, i dont see how this could be possible? can someone tell me where i went wrong

You haven't done anything wrong at this stage; the error lies elsewhere with your working or with the textbook. What is the original question?

Notice that where .

Also, you can multiply both numerator and denominator by -1 to get


Perhaps that is the "positive" answer you refer to.