Problem 61 - College Algebra

Question

Evaluate each expression without using a calculator. $$\log 100$$

Step-by-Step Solution

Answer

The value of \(\log 100\) is 2.

Step 1: Understanding the question

The operation to be performed is \(\log 100\). This is a common logarithm and therefore, the base is 10. The question requires finding the power to which 10 must be raised to get 100.

Step 2: Applying the logarithm rule

Remember that \(\log_b a = n\) is equivalent to \(b^n = a\). In this case, the question is asking to solve the equation \(10^n = 100\). Which value of \(n\) makes this equation true?

Step 3: Finding the solution

Knowing that \(10^2 = 100\), it is clear that the value of \(n\) which satisfies the equation is 2. Therefore, \(\log 100 = 2\).