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.