If x = 1, y = 2, what is the value of log(xy)?

To find the value of log(xy) when x = 1 and y = 2, you first need to substitute the values of x and y into the expression.

Calculating xy gives you:

xy = 1 * 2 = 2.

Now, you'll evaluate log(2). In the context of logarithms, log(x) typically refers to logarithm base 10 unless specified otherwise. The logarithm of 2 in base 10 is not a whole number; however, in the multiple-choice context presented, if we look at the fundamental property of logarithms, this value does not match any of the options directly provided.

If we evaluate log(xy) using the property of logarithms, we can rewrite it as:

log(xy) = log(x) + log(y).

Substituting the values in:

log(x) = log(1) = 0, since anything raised to the power of 0 results in 1.

log(y) = log(2).

Thus,

log(xy) = log(1) + log(2) = 0 + log(2) = log(2).

This means the correct evaluation gives you log(2), which does