Find log 2 with Base 8

The value of log 2 with base 8 is equal to 1/3. The logarithm of 2 with base 8 is written as log₈2, so the formula of log2 base 8 is given by

log₈2 = 1/3.

Value of log 2 base 8

Answer: The value of log 2 base 8 is equal to 1/3, that is, log₈2 = 1/3.

Explanation:

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

8 = 2³.

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

log₈2 = $\dfrac{1}{\log_2 8}$

= $\dfrac{1}{\log_2 2^3}$ as we have 8 = 2³.

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

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

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