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Express “ln va “ as a product

Express “ln √a “ as a product.
please explain how you arrived at your answer in as much detail as possible

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Jim S. | Physics (and math) are fun, reallyPhysics (and math) are fun, really
4.6 4.6 (151 lesson ratings) (151)
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Hi Kimberly,
 
ln(√a)=ln(a.5)=.5xln(a) using the general property of logs i.e. ln(xb) = bxln(x)
 
Does this help? 
 
Jim
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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 Question is not very clear.
 
   I thik you mean :
 
 
    like( ln √a ) , where a is a composite number, ( is a product of its prime factor) , i.e. 
 
      a = 12 = 2 * 2 * 3
 
    then  ln( √12) = ln √(22 * 3) = ln √22 + ln √3 = ln (22)1/2 + 1/2 ln3= ln 2 +1/2 ln 3
Lorraine T. | "Math and Science tutor for all ages" "Math and Science tutor for all ages"
5.0 5.0 (29 lesson ratings) (29)
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rule:ln(x y) = y · ln(x)
 
The natural log of the sq rt of a is the same as ln (a1/2 ) = 1/2 * ln (a)