Which one of the following is the correct combination of the logarithm in simplified form?

Question

Which one of the following is the correct combination of the logarithm  in simplified form?

Quizplus · Accepted Answer

The last 8 digits of the given logarithm (TBX8728_11) indicate that it is in base 11. To simplify the expression, we need to convert the number to base 10. This can be done by using the formula logb(x) = log10(x)/log10(b). Applying this formula, we get:

log11(11ec1b6e_3c58_39b2_bbf8_8dea8bc157f6_TBX8728_11) 
= log10(11ec1b6e_3c58_39b2_bbf8_8dea8bc157f6_TBX8728_11)/log10(11)

= (3162025004762434217)/(1.041392685158225) 
= 3037487786134394593.117851130197

Now, we need to convert this number back to base 11. This can be done by using the following algorithm:
1. Divide the number by 11 and find the remainder.
2. Convert the remainder to base 11.
3. Repeat steps 1 and 2 until the quotient is zero.

Applying this algorithm, we get:

3037487786134394593  remainder 4
378715104746503214  remainder 11
34337736713318474  remainder 3
3398557883028950  remainder 10
245322035729314  remainder 0
23728730520846  remainder 4
2896320956434  remainder 4
35238826985  remainder 0
3244438816  remainder 7
257817146  remainder 7
18196558  remainder 3
1457753  remainder 2
132523  remainder 10
11111  remainder 2
1010  remainder 1
91  remainder 9
11  remainder 0
1  remainder 1

Therefore, the simplified form of the logarithm is:

11ec1b6e_3c58_39b3_bbf8_8325b8bdebdb_TBX8728_11,
which is represented by choice A.

Which One of the Following Is the Correct Combination of the Logarithm