The value of log 2 with base 8 is equal to 1/3. The logarithm of 2 with base 8 is written as log_{8}2, so the formula of log2 base 8 is given by

log_{8}2 = 1/3.

## Value of log 2 base 8

**Answer:** The value of log 2 base 8 is equal to 1/3, that is, log_{8}2 = 1/3.

**Explanation:**

At first, we will express 8 as a power of 2. As 8 = 2×2×2, we can write

8 = 2^{3}.

Now, using the rule log_{a}b = $\dfrac{1}{\log_b a}$, it follows that

log_{8}2 = $\dfrac{1}{\log_2 8}$

= $\dfrac{1}{\log_2 2^3}$ as we have 8 = 2^{3}.

= $\dfrac{1}{3}$, obtained by using the logarithm rule: log_{a}a^{m} = m.

So the value of log 2 is equal to 1/3 when the base is 8.

**More Problems:** Value of log 8 base 2

Logarithm formulas with proofs

## FAQs

### Q1: What is log 2 base 8?

**Answer:** Log2 base 8 is equal to 1/3, that is, log_{8}2 = 1/3.