Question

Find the value of: $\log 87600+\log 23100-8 =\ ?$

• A. $\log 8.76 + \log 2.31$
• B. $\log 87.6 + \log 23.1$
• C. $\log 876 + \log 231$
• D. None of these

Hint:

Write numbers in scientific form $a\times10^n$ and use $\log(ab)=\log a+\log b$ to cancel powers of $10$ quickly.

Answer 1

The Correct Option is A

\( \log 87600 = \log(8.76 \times 10^4) = \log 8.76 + 4 \);
\( \log 23100 = \log(2.31 \times 10^4) = \log 2.31 + 4 \).
Therefore, \( \log 87600 + \log 23100 - 8 = (\log 8.76 + 4) + (\log 2.31 + 4) - 8 \)
\( \Rightarrow \log 8.76 + \log 2.31 \). \( \boxed{\log 87600 + \log 23100 - 8 = \log 8.76 + \log 2.31} \)