Final answer:
The logarithmic equation log_1,000,000 = 6 illustrates the concept that the common logarithm is the exponent to which 10 is raised to yield the number. The common logarithm of 60 is approximately 1.7782, as it is between 10 and 100, and negative logarithms result from numbers less than 1.
Step-by-step explanation:
The logarithmic equation log_1,000,000 = 6 means that 10 must be raised to the power of 6 to get 1,000,000 as a result. In general, the common logarithm of a number is the power to which 10 must be raised to equal that number. To find the common logarithm of 60, we see that 60 lies between 10 and 100, whose common logarithms are 1 and 2, respectively. Therefore, log_{10}(60) ≈ 1.7782, which is consistent with the fact that a common logarithm of a number less than 1 is negative, such as log_{10}(0.03918) ≈ -1.4069 where 0.03918 equals 10^{-1.4069}.
In the context of scientific notation, dividing large numbers or converting numbers into standard notation are operations that often require the usage of logarithms and exponentials. For example, evaluating 333,999,500,000 ÷ 0.00000000003396 would necessitate the conversion to scientific notation before performing the division.