The value of log 16 base 8 is equal to 4/3. Let us learn how to find the value of log 16 8, that is, the logarithm of 16 when the base is 8.

## What is log 16 base 8

To find the value of log 16 base 8, we will use the following formula:

log_{x} y = log_{a}y / log_{a}x.

As both 8 and 16 can be written as powers of 2, we will apply the above formula as follows:

log_{8} 16 = log_{2}16 / log_{2}8 …(∗)

We know that

16 = 2^{4}

8 = 2^{3}.

Thus from the above equation (∗), we get that

log_{8} 16 = log_{2}2^{4} / log_{2}2^{3} = 4/3, here we have used the logarithm formula: log_{a}a^{k}=k.

So the value of log16 base 8 is equal to 4/3.

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## FAQs

### Q1: What is the value of log16 8?

Answer: The value of log16 8 is equal to 4/3.