Value of log 16 base 8 | Log 16 8 Value

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_ay / log_ax.

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

log₈ 16 = log₂16 / log₂8 …(∗)

We know that

16 = 2⁴

8 = 2³.

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

log₈ 16 = log₂2⁴ / log₂2³ = 4/3, here we have used the logarithm formula: log_aa^k=k.

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

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