Value of log 8 base 2

The value of log 8 base 2 is equal to 3, that is, log₂8 =3. In this post, we will find the value of the logarithm of 8 when the base is 2.

We will now find the value of log 8 when the base is 2.

How to Find log₂8

Question: What is log8 base 2?

Answer: The value of log28 is 3.

Solution:

Step 1:

At first, we will factorize the number 8. Observe that 8 is an even number, so it is divisible by 2, and we can have

8 ÷ ${\color{red} 2}$ = 4

Again, 4 is an even number, so we have

4 ÷ ${\color{red} 2}$ = 2

Similarly,

2 ÷ ${\color{red} 2}$ = 1

Once, we get 1 we will stop and the number 8 can be written as the product of red-colored numbers. That is,

8 = 2×2×2

⇒ 8 = 2³

Step 2:

Now, taking the logarithm with base 2 on both sides, we get that

log₂8 = log₂2³

⇒ log₂8 = 3 using the logarithm rule log_bb^m = m.

Therefore the value of log 8 with base 2 is 3.

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