Final answer:
The common logarithm of 200 is found by adding the common logarithm of 100, which is 2, to the common logarithm of 2, which is approximately 0.3010, resulting in an approximate value of 2.3010.
Step-by-step explanation:
The common logarithm of a number is the power to which 10 must be raised to get that number. Since the common logarithm of 100 is 2, we know that 102 = 100. To find the common logarithm of 200, we can use the relationship between logarithms and the division of numbers. The logarithm of a number resulting from the division of two numbers is the difference between the logarithms of those two numbers. Thus, the logarithm of 200 (log(200)) can be found by using the logarithm of 100 (which is 2) and the fact that 200 is 100 times 2.
So, log(200) equals log(100×2), which is the same as log(100) + log(2). Since we know log(100) is 2, we only need to find log(2). The common logarithm of 2 is approximately 0.3010. Therefore, log(200) is approximately 2 + 0.3010 = 2.3010.
The common logarithm (log) of a number is the power to which 10 must be raised to equal that number. For example, the common logarithm of 100 is 2, because 10 must be raised to the second power to equal 100. Therefore, if the common logarithm of 100 equals 2, the common logarithm of 200 would be 2 + 0.3010 = 2.3010. This is because the logarithm of 200 can be found by adding the logarithm of 100 to the logarithm of 2.