Final answer:
The given options A to D do not correctly represent log308 in terms of a, b, and c. Using logarithm properties and the provided values, log308 can be expressed as 3*(c - (a + b)/2), which is none of the listed options.
Step-by-step explanation:
To find log308, we can use the given information: log 5=a, log 3=b, and log 2=c. According to the properties of logarithms, the logarithm of a product equals the sum of the logarithms, and the logarithm of a quotient equals the difference of the logarithms. First, we express 8 in terms of its prime factors: 8 = 23, which means that log308 = 3log302. We want to express this in terms of a, b, and c.
Since log302 = log30(60/30), we can write this as log3060 - log3030. We know that log3030 = 1 because any logarithm with a base equal to its number is 1. Now, we can express 60 in terms of its prime factors: 60 = 5 * 3 * 22. Therefore, log3060 can be written as log 5 + log 3 + 2*log 2 - log 30, and by substituting a for log 5, b for log 3, and c for log 2, we get log3060 = a + b + 2*c - 1.
As a result, log302 = (a + b + 2*c - 1) - 1 = a + b + 2*c - 2. When multiplied by 3 for log308, it becomes 3*(a + b + 2*c - 2), which can be simplified to 3a + 3b + 6c - 6. In terms of a, b, and c, the final expression for log308 is:
log308 = 3*(c - (a + b)/2)
Thus, none of the given options A to D correctly represent log308 in terms of a, b, and c.