Evaluate the sum of common logs: log 10(10) + log 10(100) + log 10(1000) + log 10(10000) + log 10(100000).

Difficulty: Easy

Correct Answer: 15

Explanation:


Introduction / Context:
This is a direct application of the definition of common logarithms on powers of 10, where log 10(10^k) = k.


Given Data / Assumptions:

  • Numbers: 10, 100, 1000, 10000, 100000 (i.e., 10^1 to 10^5)
  • Base 10 logarithms.


Concept / Approach:
Use log 10(10^k) = k and add the results.


Step-by-Step Solution:

log 10(10) = 1log 10(100) = 2log 10(1000) = 3log 10(10000) = 4log 10(100000) = 5Sum = 1 + 2 + 3 + 4 + 5 = 15


Verification / Alternative check:
No alternative needed; the identity is exact for powers of 10.


Why Other Options Are Wrong:
Expressions like log 11111 or 14·log 100 do not equal the integer sum of the exponents here; only 15 matches.


Common Pitfalls:
None significant; just ensure all logs are base 10 and recognize each term as a power of 10.


Final Answer:
15

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