Problem 14 - Algebra 2

Question

Evaluate each logarithm. $$ \log _{2} 16 $$

Step-by-Step Solution

Answer

\(\log _{2} 16 = 4\)

Step 1: Understand Logarithms

A logarithm is an operation that determines how many times a certain number, called the base, must be multiplied by itself to achieve another number. In the given logarithm \(\log _{2} 16\), the base is 2 and we need to find out how many times 2 must be multiplied by itself to get 16.

Step 2: Perform Calculations

We start with 2 and keep multiplying it by itself: \[\begin{align*}2^1 &= 2, \2^2 &= 2*2 = 4,\2^3 &= 2*2*2 = 8,\2^4 &= 2*2*2*2 = 16.\end{align*}\]So, it's clear that 2 needs to be multiplied by itself 4 times to get 16.

Step 3: Final Answer

\(\log _{2} 16 = 4\), because 2 needs to be multiplied by itself 4 times to get 16.