SOLUTION: Assume x>0 and 3x-1>0. Rewrite the following expression as a single logarithm. 2ln(x)-(1/2)ln((9x^2)-1)+ (1/2)ln (3x+1)

Question 205650: Assume x>0 and 3x-1>0. Rewrite the following expression as a single logarithm.
2ln(x)-(1/2)ln((9x^2)-1)+ (1/2)ln (3x+1)
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
Assume x>0 and 3x-1>0. Rewrite the following expression as a single logarithm.




Use the fact that  on each of the
three terms:



Use the fact that  on the first
two terms:



Use the fact that  



You actually have it as a single logarithm at this step.
However, your teacher probably wants you to simplify it.  

Put the second factor over 1 so you will have two
fractions to multiply:



Indicate the multiplication of tops and bottoms of 
those fractions:



Factor  as 



Use the fact that  to rewrite the
denominator:



Cancel:

 



Change the  power to a square root:



Edwin

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