Question

evaluate the common logarithm without the use of a calculator.
log 1000 = \square

Explanation:

Step1: Recall the definition of common logarithm

The common logarithm, denoted as $\log x$, is a logarithm with base 10, i.e., $\log_{10} x$. So we need to find the exponent to which 10 must be raised to get 1000.

Step2: Express 1000 as a power of 10

We know that $1000 = 10^3$ because $10\times10\times10 = 1000$.

Step3: Apply the logarithm property

Using the property of logarithms $\log_{a} a^b = b$, for $a = 10$ and $b = 3$, we have $\log_{10} 10^3 = 3$. So $\log 1000 = 3$.

Answer:

3