Problem 81 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

\(\log 100 = 2.\)

Step 1: Understand the problem

The problem is asking for the logarithm to the base 10 of the number 100. The logarithm to the base 10 is often written without the base, so \(\log 100\) is the same as \(\log_{10} 100\). The question is, to which power you need to raise 10 to get a result of 100.

Step 2: Logarithm Properties

One can use properties of logarithms to help solve this problem. The base of this log is 10 and we want to find the number to which 10 must be raised to equal 100. This can be formulated as the equation \(10^x = 100\).

Step 3: Simplify the expression

Looking at this equation, we clearly see that the number x that makes this equation true is 2, since \(10^2 = 100\). Therefore, \(\log_{10} 100 = 2\).