The value of log 16 base root 2 is equal to 8, that is, log_{√2}16 = 8. In this post, we will find the value of the logarithm of 16 when the base is root 2.

## How to Find log16 Base Root 2

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

**Answer:** log16 base root 2 equals 8.

**Solution:**

**Step 1:**

We know that 16 is a product of four numbers of 2’s. That is,

16 = 2×2×2×2

⇒ 16 = 2^{4} …(∗)

Next, we write 2 as a power of √2. Note that

2 = (√2)^{2}

Thus, from (∗) we get that

16 = [(√2)^{2}]^{4 }

∴ 16 = (√2)^{8 }by the rule a^{mn} = (a^{m})^{n}

**Step 2:**

Now, we take logarithms with base root 2 on both sides. By doing so we get that

log_{√2}16 = log_{√2}(√2)^{8}

⇒ log_{√2}16 = 8, Here we have used the logarithm formula: log_{a}a^{k} = k.

**So the value of log 16 base root 2 is 2.**

**Have You Read These Logarithms?**

## FAQs

### Q1: What is the value of log 16 when base is root 2?

Answer: As 16=(√2)^{8}, the logarithm of 16 with base root 2 is equal to 8.