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?

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) (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Break up the log using the identity

Break up the first log using the identity

Convert to rational exponent notation.

Pull down the exponents using the identity

So
Answer by jsmallt9(3759) (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?

If yes, keep reading. If not, then please repost your problem with properly balanced parentheses.

Your answer, , is pretty close. One error is that it should be a difference instead of the sum because of the division in the original log:

This may meet the requirements of the problem. But it is possible to use the property, , on the first log giving:

I don't know if this last expression would be preferred over .

RELATED QUESTIONS
Use properties of logarithms to rewrite each expression as the sum, difference, or... (answered by solver91311)
I need to write this problem as a single log:... (answered by erica65404)
Assume x>0 and 3x-1>0. Rewrite the following expression as a single logarithm.... (answered by Edwin McCravy)
I have two questions I need help with 1) how do I solve 5^2x-1=169. this is part of the... (answered by solver91311)
Write the logarithmic expression as a sum or difference of logarithms. ln [(2x sqrt... (answered by ikleyn)
Here is my problem: Write the expression as a single logarithm... (answered by stanbon)
Use the logarithmic properties to rewrite the expression as a sum difference, and/or... (answered by Tatiana_Stebko)
1) solve the logarithm equation for x: 2ln 3x =8 2) solve the exponential... (answered by Alan3354)
How do I write the expression as the logarithm of a single quantity for : {{{ ln 2 +... (answered by Alan3354)