SOLUTION: Rewrite as a sum and/or difference of multiples of logarithms: ln((3x^2)/square root 2x+1))....my answer was 2ln(3x) + 1/2ln(2x+1) is this correct?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Rewrite as a sum and/or difference of multiples of logarithms: ln((3x^2)/square root 2x+1))....my answer was 2ln(3x) + 1/2ln(2x+1) is this correct?      Log On


   

Question 240493: Rewrite as a sum and/or difference of multiples of logarithms:
ln((3x^2)/square root 2x+1))....my answer was 2ln(3x) + 1/2ln(2x+1) is this correct?
Found 2 solutions by jim_thompson5910, jsmallt9:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28%283x%5E2%29%2F%28sqrt%282x%2B1%29%29%29 Start with the given expression.


ln%283x%5E2%29-ln%28sqrt%282x%2B1%29%29 Break up the log using the identity ln%28x%2Fy%29=ln%28x%29-ln%28y%29


ln%283%29%2Bln%28x%5E2%29-ln%28sqrt%282x%2B1%29%29 Break up the first log using the identity ln%28xy%29=ln%28x%29%2Bln%28y%29


ln%283%29%2Bln%28x%5E2%29-ln%28%282x%2B1%29%5E%281%2F2%29%29%5E%22%22 Convert to rational exponent notation.


ln%283%29%2B2%2Aln%28x%29-%281%2F2%29ln%282x%2B1%29 Pull down the exponents using the identity ln%28x%5Ey%29=y%2Aln%28x%29


So

Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
You have unbalanced parentheses in your problem so I have to check. Is this the original logarithm?
ln%28%283x%5E2%29%2Fsqrt%282x%2B1%29%29
If yes, keep reading. If not, then please repost your problem with properly balanced parentheses.

Your answer, 2ln%283x%29+%2B+%281%2F2%29ln%282x%2B1%29, is pretty close. One error is that it should be a difference instead of the sum because of the division in the original log:
ln%28%283x%5E2%29%2Fsqrt%282x%2B1%29%29+=+2ln%283x%29+-+%281%2F2%29ln%282x%2B1%29
This may meet the requirements of the problem. But it is possible to use the property, log%28a%2C+%28p%2Aq%29%29+=+log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29, on the first log giving:

I don't know if this last expression would be preferred over 2ln%283x%29+-+%281%2F2%29ln%282x%2B1%29.