Express “ln √a “ as a product.

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

Express “ln √a “ as a product.

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

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Fairport, NY

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

Woodland Hills, CA

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 √(2^{2} * 3) = ln √2^{2} + ln √3 = ln (2^{2})^{1/2} + 1/2 ln3= ln 2 +1/2 ln 3

Jackson, MI

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)

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