Final answer:
To find log30 8, we can use the properties of logarithms and the given values of a, b, and c. We know that log 5 = a, log 3 = b, and log 2 = c. By rewriting 30 as a product of factors whose logarithms are known, we can find log30 8.
Step-by-step explanation:
To find log30 8, we can use the properties of logarithms and the given values of a, b, and c. We know that log 5 = a, log 3 = b, and log 2 = c. We need to find log30 8.
We can rewrite 30 as a product of factors whose logarithms are known. Since 30 = 2 x 3 x 5, we can rewrite log30 8 as log(2 x 3 x 5) 8. Using the properties of logarithms, we can expand this expression as log2 8 + log3 8 + log5 8.
Since log2 8 = 3c, log3 8 = 2b, and log5 8 = 3a, we can substitute the given values of a, b, and c. Therefore, log30 8 = 3c + 2b + 3a.