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1. If $\log_{10} 7 = a,$ then $\log_{10} (\frac{1}{70})$ is equal to

A. - (1 + a)

B. (1 + a)^-1

C. $\frac{a}{10}$

D. $\frac{1}{10 a}$

Solution:

\begin{aligned} \log_{10} (\frac{1}{70}) \\ = \log_{10} 1 - \log_{10} 70 \\ = - \log_{10} (7 \times 10) \\ = - (\log_{10} 7 + \log_{10} 10) \\ = - (a + 1) \end{aligned}

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