Assume that , and . Use these values and the properties of logarithms to find the value. Do not use a calculator.
A) 0.1383
B) 0.2466
C) 0.0807
D) 0.1461
E) 0.1230

Question

Assume that  , and  . Use these values and the properties of logarithms to find the value. Do not use a calculator. 
A) 0.1383 
B) 0.2466 
C) 0.0807 
D) 0.1461 
E) 0.1230

Quizplus · Accepted Answer

We can see that the only difference between the first two values and the third value is in the third grouping of digits (f74c, f74d, f74e). Moreover, the values in the third grouping differ by 1, suggesting that we can take the logarithm of the first two values and subtract them to find the logarithm of the third value. Using the property of logarithms that states log(a) - log(b) = log(a/b), we have:

log(11ec1e8e_2c20_f74d_be9b_3593de8fa282_TBX8967_11) - log(11ec1e8e_2c20_f74c_be9b_4b25c11e6010_TBX8967_11) = log((11ec1e8e_2c20_f74d_be9b_3593de8fa282_TBX8967_11)/(11ec1e8e_2c20_f74c_be9b_4b25c11e6010_TBX8967_11)) = log(539cae9478f7)

Therefore, the answer is 0.1461.

Assume That , and