Evaluate the sum of common logs: log 10(10) + log 10(100) + log 10(1000) + log 10(10000) + log 10(100000).
Aptitude
Logarithm
Difficulty: Easy
Choose an option
-
A15
-
Blog 11111
-
Clog10 1111
-
D14 log10 100
-
ENone of these
Answer
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 = 15Verification / 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