Problem 51 - Algebra 2

Question

Evaluate each logarithm. $$ \log _{4} 64 $$

Step-by-Step Solution

Answer

The logarithm \(\log _{4} 64\) is equal to 3.

Step 1: Understanding logarithm notation

The logarithm notation \( \log {4} {64} \) means that we are trying to find a number that, when 4 is raised to the power of that number, will give 64. In notation format, this can be written as: \( 4^x = 64 \)

Step 2: Finding power of base

Now we need to find 'x' that satisfy \( 4^x = 64 \). We know that \( 4^3 = 64 \). Therefore, x = 3.

Step 3: Writing solution

Now that we found our value of x, we can write our solution. The evaluation of \( \log {4} {64} \) is 3