Value of log 16 base root 2

The value of log 16 base root 2 is equal to 8, that is, log_√216 = 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 = 2⁴ …(∗)

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_√216 = log_√2(√2)⁸

⇒ log_√216 = 8, Here we have used the logarithm formula: log_aa^k = k.

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

Have You Read These Logarithms?

log 16 base 2

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