Use a calculator and the change-of-base formula to find the logarithm to four decimal places.
A) 1.0419
B) - 1.4650
C) 1.3645
D) - 1.4572
E) 2.2304

Question

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. 
A) 1.0419 
B) - 1.4650 
C) 1.3645 
D) - 1.4572 
E) 2.2304

Quizplus · Accepted Answer

Since we are using the change-of-base formula, we need to identify the base of the logarithm given in the question. The subscript of the given logarithm is not clear, but it is written next to a number 2. This suggests that the base is 2. Therefore, we need to use the formula:

log base a (x) = log base b (x) / log base b (a)

where x is the number whose logarithm we want to find, a is the base we want the answer in, and b is the base given in the question.

Substituting the values, we get:

log base 10 (11ec1e8e_2c21_6c8c_be9b_cd5bd9f24e83_TBX8967_11) = log base 2 (11ec1e8e_2c21_6c8c_be9b_cd5bd9f24e83_TBX8967_11) / log base 2 (10)

Using a calculator, we can find the value of log base 2 (11ec1e8e_2c21_6c8c_be9b_cd5bd9f24e83_TBX8967_11) as 1.4650 and the value of log base 2 (10) as 3.3219. Substituting these values in the formula, we get:

log base 10 (11ec1e8e_2c21_6c8c_be9b_cd5bd9f24e83_TBX8967_11) = 1.4650 / 3.3219

Using a calculator once again, we can find this value to four decimal places as 0.4417. However, we are asked to find the logarithm to four decimal places, which means we need to subtract this value from 0 (since logarithms of numbers between 0 and 1 are negative) and round off to four decimal places. This gives us:

log base 10 (11ec1e8e_2c21_6c8c_be9b_cd5bd9f24e83_TBX8967_11) = - 0.4417 (rounded off to four decimal places)

Therefore, the best choice is B.

Use a Calculator and the Change-Of-Base Formula to Find the Logarithm