Evaluate \(\log_{10} 25 + \log_{10} 32 - \log_{10} 8\)
Question 1 Report
Evaluate \(\log_{10} 25 + \log_{10} 32 - \log_{10} 8\)
Answer Details
We can use the following property of logarithms:
- \(\log_{a}b + \log_{a}c = \log_{a}(bc)\)
- \(\log_{a}b - \log_{a}c = \log_{a}\left(\dfrac{b}{c}\right)\)
Using this property, we can rewrite the expression as:
\begin{align*}
\log_{10} 25 + \log_{10} 32 - \log_{10} 8 &= \log_{10}(25\cdot 32) - \log_{10} 8 \\
&= \log_{10}(800) - \log_{10} 8 \\
&= \log_{10}\left(\frac{800}{8}\right) \\
&= \log_{10}(100) \\
&= 2
\end{align*}
Therefore, the value of the expression is 2. Thus, the answer is (2).
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