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What is the value of this expression? log 2 8 + log 3 (1/3)

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Final answer:

To solve the expression log₂ 8 + log₃ (1/3), we recognize that log₂ 8 is 3 and log₃ (1/3) is -1. Adding these values gives us 2.

Step-by-step explanation:

To find the value of the expression log₂ 8 + log₃ (1/3), we need to apply the properties of logarithms. The logarithm of a number to the base that is the same as that number equals 1. Therefore, log₂ 8 simplifies to 3 because 23 = 8. Additionally, the logarithm of a reciprocal is the negative of the logarithm of the number itself, so log₃ (1/3) simplifies to -1 because 3-1 = 1/3. Adding these two values together, we get 3 + (-1) = 2. Ultimately, the expression evaluates to 2 through these log properties, facilitating a more straightforward calculation.

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