Final answer:
Log 1000 simplifies to 3 because 10 raised to the power of 3 is equal to 1000.
Step-by-step explanation:
To evaluate or simplify the expression log 1000 without using a calculator, we can connect to the concept of integer powers. The logarithm of a number is the exponent to which the base must be raised to obtain that number. Since the base is understood to be 10 in common logarithms, we look for the power to which 10 must be raised to give us 1000.
Here, we recognize that 10³ equals 1000, because when we multiply 10 by itself three times (10 × 10 × 10), we get 1000. Therefore, log 1000 is equal to 3 because 10 raised to the power of 3 gives us 1000.