Problem 28 - Precalculus : Building Concepts and Connections

Question

Evaluate each expression without using a calculator. $$\log _{7} 49$$

Step-by-Step Solution

Answer

The value of the expression \(\log_{7} 49\) is 2.

Step 1: Understand the logarithm property

The formula \(\log_b (a) = n\) means that \(b^n = a\). Therefore, we need to understand which power we have to raise the base (7) to get the number under the logarithm (49).

Step 2: Calculate the Logarithm

Remember, we need power to which we must raise 7 (base) to get 49. So, when 7 is raised to the power 2 (7*7), we obtain 49. Therefore, \(\log_{7} 49 = 2\).