Final answer:
The simplified form of the expression 2*log(x) - (3*log(y) + log(y)) is log(x^2/y^4) using properties of logarithms such as the logarithm of a product, division, and exponentiation.
Step-by-step explanation:
To simplify the expression 2*log(x) - (3*log(y) + log(y)), we can apply several properties of logarithms. The logarithm of a product of two numbers is the sum of the logarithms of the two numbers. Similarly, the logarithm of a division is the difference between the logarithms of the numerator and the denominator. Also, the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.
Using these properties, we can rewrite the expression as 2*log(x) - 4*log(y), which can be further simplified using the division property to log(x^2/y^4).