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Chapter 3: Problem 18

Evaluate the indicated expression. Do not use a calculator for these exercises. $$ \log \frac{1}{1000} $$

Short Answer

Expert verified
\(\log{\frac{1}{1000}} = -3\)

Step by step solution

01

Rewrite (1/1000) as a power of 10

We need to rewrite \(\frac{1}{1000}\) as a power of 10, i.e., find an exponent n such that \(10^n = \frac{1}{1000}\). Notice that \(1000 = 10^3\), so we can write \(\frac{1}{1000} = \frac{1}{10^3} = 10^{-3}\), where we used the property \(a^{-n} = \frac{1}{a^n}\).
02

Find the logarithm

Since we have found that \(10^{-3} = \frac{1}{1000}\), the logarithm (base 10) of \(\frac{1}{1000}\) is equal to the exponent -3: \(\log{\frac{1}{1000}} = \log{10^{-3}} = -3\). So, the final answer is: \(\log{\frac{1}{1000}} = -3\).

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