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

log_{4}16 = 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 = 4^{2}

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

log_{4}16 = log_{4}4^{2}

⇒ log_{4}16 = 2 log_{4}4 as we know log_{a}b^{n} = n log_{a}b.

⇒ log_{4}16 = 2 × 1, because log_{a}a =1.

⇒ log_{4}16 = 2.

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

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## FAQs

### Q1: What is log 16 with base 4?

**Answer:** As 16=4^{2}, log 16 with base 4 is equal to 2, that is, log_{4}16 = 2.