Express “ln va “ as a product

Question

Express “ln √a “ as a product

Answer 1

Express “ln va “ as a product

Solution:

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from x^a/b = r(b) [x^a], where r = root, and r(b) = root of index b; a = exponent

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from our example: va = r(2) [a] = a^1/2

and using logarims law: Ln [a^b/c] = (b/c) * ln [a], then

ln va = ln ( a^1/2) = (1/2)*ln [a] = ln[a] / 2

 

Answer 2

Logarithm of a number raised to a power can be expressed as the power * logarithm of the number

 

Expressed Algebraically, log(x^a) = a * log(x)

 

ln is natural logarithm which is a logarithm to base e (natural number)

 

The given expression ln(√a) can be expressed as ln(a^0.5)

 

This can be expressed as a product as 0.5 * ln(a)