Express “ln va “ as a product

Question

Express “ln √a “ as a product.

please explain how you arrived at your answer in as much detail as possible

Answer 1

 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

Answer 2

rule:ln(x ^y) = y · ln(x)

 

The natural log of the sq rt of a is the same as ln (a^1/2 ) = 1/2 * ln (a)

Answer 3

Hi Kimberly,

 

ln(√a)=ln(a^.5)=.5xln(a) using the general property of logs i.e. ln(x^b) = bxln(x)

 

Does this help? 

 

Jim