Question

1. evaluate the logarithm. \\(\log_{10} 0.001 = \square\\)

Explanation:

Step1: Recall the definition of logarithm

The logarithm \(\log_{b}a = x\) is equivalent to \(b^{x}=a\). For \(\log_{10}0.001\), we need to find \(x\) such that \(10^{x}=0.001\).

Step2: Rewrite 0.001 as a power of 10

We know that \(0.001=\frac{1}{1000}=\frac{1}{10^{3}} = 10^{- 3}\).

Step3: Solve for x

Since \(10^{x}=10^{-3}\), by the property of exponential functions (if \(a^{m}=a^{n}\), then \(m = n\) for \(a>0,a
eq1\)), we get \(x=-3\). So \(\log_{10}0.001=-3\).

Answer:

\(-3\)