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Suppose logᵦ(3)=0.2 and logᵦ(13)=0.5. Use the properties of logarithms to find: logᵦ(39)

User Trusktr
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Final answer:

To calculate logβ(39), apply the property of logarithms regarding products: logβ(39) = logβ(3×13) = logβ(3) + logβ(13) = 0.2 + 0.5 = 0.7.

Step-by-step explanation:

The subject of this question is Mathematics, and it involves using the properties of logarithms to find the logarithm of a product of numbers for which the logarithms are known: logβ(3)=0.2 and logβ(13)=0.5.

To find logβ(39), we notice that 39 is the product of 3 and 13. By the property of logarithms that states the logarithm of a product is equal to the sum of the logarithms of the factors (logβ(ab) = logβ(a) + logβ(b)), we can find logβ(39) by summing the given logarithms:

logβ(39) = logβ(3×13) = logβ(3) + logβ(13) = 0.2 + 0.5 = 0.7

Therefore, logβ(39) is equal to 0.7.

User Alessandroempire
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