How do you expand log(1/2)(3x^2/2) using properties and rules for logarithms?

The expression is .

If the argument is a rational expression, like in our case: , we convert the expressions or numbers in the numerator into sums, and subtract the ones in the denominator.

For example: .

So, our logarithm can be expanded as .

We also have the rule .

Thus, using this rule we can perform the following simplifications: