Problem 24 - Introductory and Intermediate Algebra for College Students 4th

Question

Evaluate each expression without using a calculator. $$\log _{3} 27$$

Step-by-Step Solution

Answer

The value of \(\log_{3} 27\) is 3.

Step 1: Identifying base and number

In the expression \(\log_{3} 27\), 3 is the base and 27 is the number. A logarithm answers the question: 'To what exponent should we raise the base to obtain the number?'.

Step 2: Finding the exponent

\(\log_{3} 27\) asks: '3 to what power equals 27?'. Evaluate the exponent required. By knowledge of basic exponent rules, we find that \(3^{3} = 27\). So, the exponent required is 3.