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Logarithm of a power

The logarithm of a power is

log_a (xⁿ) = n log_a x

 

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Explanation

From the logarithm of a product follows that

log_a (xⁿ) = log_a (x · x · x ··· x) = log_a x + log_a x + ··· + log_a x = n log_a x

 

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Example 1

You can see that ln (e²) = 2, because

ln (e²) = 2 ln (e) = 2

 

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Example2

You can see that ln (√a) = ½ ln (a), because

ln (√a) = ln (a^1/2) = ½ ln (a)

 

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