Value of log 16 base 2

The value of log 16 with base 2 is equal to 4, that is, log₂16 =4. In this post, we will find the value of the logarithm of 16 when the base is 2.

How do you Find log₂16

Question: What is log16 base 2?

Answer: log216 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 = 2⁴

Step 2:

log₂16 = log₂2⁴

⇒ log₂16 = 4 log₂2 ( using the logarithm formula log_ab^k = k log_ab )

Now, we use log_aa=1. So

 log₂16 = 4.

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

Video Solution of log16 base 2:

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Value of log₄ 16 : The value of log 16 base 4 is equal to 2.

Value of log₂ 8 : The value of log 8 base 2 is equal to 3.

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