SOLUTION: Write the expression as a logarithm of a single quantity 3/2[ln(x2+1)-ln(x+1)-ln(x-1)]

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Question 279768: Write the expression as a logarithm of a single quantity
3/2[ln(x2+1)-ln(x+1)-ln(x-1)]
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%283%2F2%29%28ln%28x%5E2%2B1%29-ln%28x%2B1%29-ln%28x-1%29%29
We can use a property of logarithms, log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Fq%29%29, to combine the first two logarithms:
%283%2F2%29%28ln%28%28x%5E2%2B1%29%2F%28x%2B1%29%29-ln%28x-1%29%29
We can use that property again to combine the remaining logarithms:
%283%2F2%29%28ln%28%28%28x%5E2%2B1%29%2F%28x%2B1%29%29%2F%28x-1%29%29%29
which simplifies as follows:
%283%2F2%29%28ln%28%28x%5E2%2B1%29%2F%28%28x%2B1%29%2A%28x-1%29%29%29%29
%283%2F2%29%28ln%28%28x%5E2%2B1%29%2F%28x%5E2-1%29%29%29
This is a single term and may be an acceptable answer. But your teacher probably wants you to use another property of logarithms, q%2Alog%28a%2C+%28p%29%29+=+log%28a%2C+%28p%5Eq%29%29, to move the 3/2 from in front into the argument as an exponent:
ln%28%28%28x%5E2%2B1%29%2F%28x%5E2-1%29%29%5E%283%2F2%29%29