WEBVTT

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Here is the problem: Evaluate log base 9 of 27.

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Evaluate the logarithm of 27 with base 9.

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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 27 equals 9 to the power 3 over 2).

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So the answer is log 9(27) equals 3 over 2.

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9 raised to 3 over 2 gives 27 exactly.

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Check: 9 to the power 1.5 approximately 27.