WEBVTT

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Here is the problem: Evaluate log base 10 of 0.001.

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Evaluate the logarithm of 1 over 1000 with base 10.

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Ask: what power of the base gives the number?

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Write both numbers as powers of the same prime factors. Comparing prime exponents shows 1 over 1000 equals 10 to the power negative 3.

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So the answer is ln(1 over 1000) equals negative 3.

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10 raised to negative 3 gives 1 over 1000 exactly.

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Check: 10 to the power negative 3 approximately 0.001.