Final answer:
To simplify the expression 2 log(4) + 1/2 log(9) - 3 log(x), we use the properties of logarithms. The expression simplifies to log(48/x^3).
Step-by-step explanation:
To simplify the expression 2 log(4) + 1/2 log(9) - 3 log(x), we can first apply the property of logarithms that states log(ab) = log(a) + log(b). Using this property, we can rewrite the expression as log(4^2) + log(9^(1/2)) - log(x^3). Simplifying further, we get log(16) + log(3) - log(x^3).
The next step is to apply the property that states log(a/c) = log(a) - log(c). So, we have log((16 * 3) / x^3).
Finally, we can simplify the expression as log(48/x^3), which is the simplified form of the given expression.