Question

evaluate the following logarithmic expression without the use of a calculator. write your answer as a fraction reduced to lowest terms.
log(0.001)
answer
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Explanation:

Step1: Recall log base 10

The logarithm \(\log(x)\) here is base 10 (common logarithm). So we need to find \(y\) such that \(10^y = 0.001\).

Step2: Express 0.001 as power of 10

We know that \(0.001=\frac{1}{1000}=\frac{1}{10^3}=10^{-3}\). So if \(10^y = 10^{-3}\), then by the property of exponents (if \(a^m=a^n\), then \(m = n\) for \(a>0,a
eq1\)), we get \(y=- 3\).

Answer:

\(-3\) (or as a fraction \(\frac{-3}{1}\))