Final answer:
The logarithmic expressions in numerical order from smallest to largest are: log 1, log 0.02, log, 9, log, 27, log2 900. So, the sequence is (B) log 1, (C) log 0.02, (D) log, 9, (E) log, 27, and (A) log2 900.
Step-by-step explanation:
The logarithmic expressions in numerical order from smallest to largest are as follows:
(B) log 1, (C) log 0.02, (D) log, 9, (E) log, 27, (A) log2 900
The expression (B) log 1 has the smallest value because the logarithm of 1 to any base is always 0.
The expression (C) log 0.02 has the next smallest value. Logarithms of numbers between 0 and 1 are negative, so log 0.02 is a negative value.
The expression (D) log, 9 has a larger value since logarithms of numbers greater than 1 are positive. log, 9 is positive because 10 raised to a power is 9.
The expression (E) log, 27 is larger than log, 9 because 10 raised to a power is 27.
The expression (A) log2 900 has the largest value.
The base 2 logarithm of 900 is larger than log, 27 because 2 raised to a power is 900.
Thus, the sequence is (B) log 1, (C) log 0.02, (D) log, 9, (E) log, 27, and (A) log2 900.