Value of log 16 base 4 | Find log_4 16

The value of log 16 base 4 is equal to 2. The logarithm of 16 to the base is expressed as log₄16, and its formula is given by

log₄16 = 2.

Find log 16 to the base 4

Answer: The value of logarithm of 16 to the base 4 is 2.

Explanation:

We know that

16 = 4×4

⇒ 16 = 4²

Now, taking logarithms with base 4 on both sides, we get that

log₄16 = log₄4²

⇒ log₄16 = 2 log₄4 as we know log_abⁿ = n log_ab.

⇒ log₄16 = 2 × 1, because log_aa =1.

⇒ log₄16 = 2.

So the value of log 16 to the base 4 is equal to 2.

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