Problem 23 - College Algebra Essentials

Question

Evaluate each expression without using a calculator. $$\log _{2} 64$$

Step-by-Step Solution

Answer

The logarithm base 2 of 64 equals to 6.

Step 1: Understand the Question

The question is asking for the value of \(\log _{2} 64\). The task requires to find the value to which 2 (the base) needs to be raised to get 64.

Step 2: Use the Definition of Logarithms

In logarithms, \(\log_b a = c\) means that \(b^c = a\). In our case, we need to find a number \(c\) such that \(2^c = 64\).

Step 3: Calculate the Exponent

By knowing the powers of 2, it can be determined that \(2^6 = 64\) Therefore, \(c = 6\). This means that \(\log _{2} 64 = 6\).