WEBVTT

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Here is the problem: Evaluate log base 5 of 0.2.

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Evaluate the logarithm of 1 over 5 with base 5.

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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 5 equals 5 to the power negative 1.

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So the answer is log 5(1 over 5) equals negative 1.

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5 raised to negative 1 gives 1 over 5 exactly.

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Check: 5 to the power negative 1 approximately 0.2.