The value of log 16 with base 2 is equal to 4, that is, log_{2}16 =4. In this post, we will find the value of the logarithm of 16 when the base is 2.

## How do you Find log_{2}16

**Question: What is log16 base 2?**

Answer: log_{2}16 is equal to 4. |

**Solution:**

**Step 1:**

At first, we will factorize the number 16. To do so, we will start dividing 16 by prime numbers.

16 ÷ ${\color{red}2}$ = 8

8 ÷ ${\color{red}2}$ = 4

4 ÷ ${\color{red} 2}$ = 2

2 ÷ ${\color{red}2}$ = 1

So 16 will be equal to the red-numbered numbers. Thus,

16 = 2 × 2 × 2 × 2.

As 16 is a product of four copies of 2’s, we get that

16 = 2^{4}

**Step 2:**

log_{2}16 = log_{2}2^{4}

⇒ log_{2}16 = 4 log_{2}2 ( using the logarithm formula log_{a}b^{k} = k log_{a}b )

Now, we use log_{a}a=1. So

log_{2}16 = 4.

**Conclusion:** So 4 is the value of log 16 when the base is 2.

**Video Solution of log16 base 2:**

Have You Read These?

Value of log_{4} 16 : The value of log 16 base 4 is equal to 2.

Value of log_{2} 8 : The value of log 8 base 2 is equal to 3.

## FAQs

**Q1: What is the value of log**_{2}16?

_{2}16?

Answer: As 16 = 2^{4}, the value of log_{2}16 is equal to 4.