Question

evaluate the expression without using a calculator.
log 1000
log 1000 = \square

Explanation:

Step1: Recall the definition of logarithm

The common logarithm \(\log x\) is base - 10, so \(\log_{10}x=y\) means \(10^{y}=x\). We need to find \(y\) such that \(10^{y} = 1000\).

Step2: Express 1000 as a power of 10

We know that \(1000=10\times10\times10 = 10^{3}\). So we have the equation \(10^{y}=10^{3}\).

Step3: Use the property of exponents

If \(a^{m}=a^{n}\) (where \(a>0,a
eq1\)), then \(m = n\). Since \(10^{y}=10^{3}\) and \(a = 10\), we can conclude that \(y = 3\). So \(\log_{10}1000=3\).

Answer:

\(3\)