WEBVTT

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Here is the problem: Evaluate log base 2 of 1 over 32.

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Evaluate the logarithm of 1 over 32 with base 2.

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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 32 equals 2 to the power negative 5.

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So the answer is log 2(1 over 32) equals negative 5.

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2 raised to negative 5 gives 1 over 32 exactly.

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Check: 2 to the power negative 5 approximately 0.03125.