Problem 23 - College Algebra

Question

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

Step-by-Step Solution

Answer

The value of \(\log_{2}64\) is 6.

Step 1: Understand the Logarithm

Logarithms are the inverse of exponentiation. The expression \(\log_{2}64\) reads 'log base 2 of 64', and it represents the exponent to which we have to raise the base (2) to get the number (64).

Step 2: Express the Number as Power of Base

64 can be expressed as a power of 2. In fact, \(2^{6} = 64\).

Step 3: Identify the Exponent

It is clear that when we express 64 as \(2^{6}\), the exponent is 6. Since logarithm is asking for the exponent, we can conclude that \(\log_{2}64 = 6\).