QuestionJuly 15, 2025

Find the common logarithm without using your calculator. log100000 square

Find the common logarithm without using your calculator. log100000 square
Find the common logarithm without using your calculator. log100000 square

Solution
4.1(171 votes)

Answer

5 Explanation 1. Identify the base of the common logarithm The common logarithm is base 10, so log_{10}100000. 2. Express the number as a power of 10 100000 = 10^5. 3. Apply the logarithm power rule **log_{b}(a^n) = n \cdot log_{b}(a)**. Thus, log_{10}(10^5) = 5 \cdot log_{10}(10). 4. Simplify using the identity Since log_{10}(10) = 1, it simplifies to 5 \cdot 1 = 5.

Explanation

1. Identify the base of the common logarithm<br /> The common logarithm is base 10, so $log_{10}100000$.<br />2. Express the number as a power of 10<br /> $100000 = 10^5$.<br />3. Apply the logarithm power rule<br /> **$log_{b}(a^n) = n \cdot log_{b}(a)$**. Thus, $log_{10}(10^5) = 5 \cdot log_{10}(10)$.<br />4. Simplify using the identity<br /> Since $log_{10}(10) = 1$, it simplifies to $5 \cdot 1 = 5$.
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