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

## How to Find log_{4}16

**Question: What is log16 base 4?**

Answer: The value of log_{4}16 is 2. |

**Solution:**

**Step 1:**

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

16 is an even number, so it is divisible by 2, and we write

16 ÷ ${\color{red} 2}$ = 8

Again, 8 is an even number, so we have

8 ÷ ${\color{red} 2}$ = 4

Similarly,

4 ÷ ${\color{red} 2}$ = 2

2 ÷ ${\color{red} 2}$ = 1

Once, we get 1 we will stop. Then 16 can be written as the product of red-colored numbers. Thus,

16 = 2×2×2×2

⇒ 16 = 2^{4} = (2^{2})^{2 }using the rule a^{mn} = (a^{m})^{n}

⇒ 16 = 4^{2}

**Step 2:**

Now, taking the logarithm with base 4 on both sides, we get that

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

⇒ log_{4}16 = 2 using the logarithm rule log_{a}a^{k} = k.

**So the value of log 16 with base 4 is 2.**

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## FAQs

### Q1: What is the value of log 16 when base is 4?

Answer: As 16=4^{2}, the logarithm of 16 with base 4 is equal to 2.