Final answer:
To simplify the given expression, we can use the properties of logarithms. The logarithm of a product is equal to the sum of the logarithms of the factors, and the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. Therefore, the equivalent expression is 3 - log3 2.
Step-by-step explanation:
To simplify the given expression, we can use the properties of logarithms. The logarithm of a product is equal to the sum of the logarithms of the factors, and the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator.
Using these properties, we can rewrite the expression as follows:
3log28 + 4log2(1/2) - log32
= log283 + log2(1/2)4 - log32
= log2(23) + log2(1/2)4 - log32
= log223 + log214 - log32
= 3 + 4(0) - log32
= 3 - log32
So, the simplified expression is 3 - log32.