Final answer:
To find log3(27/x), use the properties of logarithms. Since log3(27) is equivalent to 3, and assuming x=1 so that log3(x) equals 1, the result is 3 - 1 = 2, which is not available in the provided answer options.
Step-by-step explanation:
The question asks to find the value of log3 (27/x) given that log(3) = 1.77. To solve for this, we can use the properties of logarithms.
First, we notice that 27 is 3 to the power of 3, which makes it log327 = log333 = 3 (since log33 = 1).
Now, applying the quotient rule of logarithms, log3 (27/x) can be written as log327 - log3x. Plugging in log327 = 3, we get 3 - log3x.
We are given log(3) = 1.77. Knowing that x has to be 3 to render the expression 3 - log3x equal to one of the provided options (A, B, C, or D), we can see that x must be 1, since log33 = 1. So, the answer would be 3 - 1 = 2. Hence, the value of log3 (27/x) is 2, which is not listed among the answer choices provided.