Final answer:
To find log 1/2 using the properties of logarithms, we note that log 1 is 0 and we deduce that log 2 is 0.3 based on the given value of log 8. Subtracting these values gives us log 1 - log 2 = 0 - 0.3 = -0.3.
Step-by-step explanation:
The goal is to find log 1/2 using the properties of logarithms and the given values: log 12 = 1.1, log 8 = 0.9, and log 7 = 0.8. The properties of logarithms tell us that the logarithm of a quotient (division of two numbers) is the difference between the logarithms of the numerator and the denominator (log a/b = log a - log b). Thus, to find log 1/2, we can use the fact that 1/2 is the same as 1 divided by 2.
We can start with the concept that the logarithm of 1 is always 0, and then subtract the logarithm of 2 from it. To find the logarithm of 2, we can use the given log 8 value. Since 8 is 2³, log 8 is 3 times log 2. Since we are given that log 8 = 0.9, we can set up the equation log 2 = log 8 / 3 = 0.9 / 3. Therefore, log 2 = 0.3.
Now, we can find log 1/2 using the property that log(1/2) = log 1 - log 2. Substituting the values, we get log 1/2 = 0 - 0.3 = -0.3. Therefore, the correct setup to find log 1/2 among the given options is B) log 1 - log 2 = 0 - 0.3 = -0.3.