Evaluate \(\log_{10}(\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)
Question 1 Report
Evaluate \(\log_{10}(\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)
Answer Details
To simplify this expression, we can first use the identity:
$$\log_{a}(b) + \log_{a}(c) = \log_{a}(bc)$$
Using this identity, we can simplify the given expression as follows:
\begin{align*}
\log_{10}\left(\frac{1}{3}+\frac{1}{4}\right) + 2\log_{10}(2) + \log_{10}\left(\frac{3}{7}\right) &= \log_{10}\left(\frac{7}{12}\right) + \log_{10}(2^2) + \log_{10}\left(\frac{3}{7}\right) \\
&= \log_{10}\left(\frac{7}{12} \cdot 2^2 \cdot \frac{3}{7}\right) \\
&= \log_{10}(1) \\
&= 0
\end{align*}
Therefore, the answer is 0.
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