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Here is the problem: Evaluate log base 3 of 81.

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Evaluate the logarithm of 81 with base 3.

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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 81 equals 3 to the power 4.

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So the answer is log 3(81) equals 4.

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3 raised to 4 gives 81 exactly.

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Check: 3 to the power 4 approximately 81.