Final answer:
To simplify log4256, we use the property of logarithms to find that it equals 4, because 256 is 4 raised to the fourth power and the logarithm of a number to the base of itself is always 1.
Step-by-step explanation:
The question asks to simplify log4256. We use the fact that if a is a positive number and ax = y, then logay = x. In other words, the logarithm gives the power to which the base must be raised to get the number.
256 can be expressed as 4 raised to some power since 256 is a power of 4. This is because 256 = 44. Therefore, log4256 = log444. By the laws of logarithms, this simplifies to 4, because log444 = 4 × log44, and log44 = 1 since 4 is the base of the logarithm itself.