The value of log 81 base 3 is equal to 4. As log 81 base 3 is written as log_{3}81, we have that log_{3}81 =4. In this post, we will learn how to find the logarithm of 81 with base 3.

The formula of the logarithm of 81 with base 3 is given as follows:

log_{3}81 =4.

## Find log 81 with base 3

**Answer:** The logarithm of 81 to the base 3 is equal to 4.

**Explanation:**

As 81 = 3×3×3×3, we have that 81=3^{4}.

So, log_{3}81 = log_{3}3^{4}

⇒ log_{3}81 = 4 log_{3}3 by the logarithm formula: log_{a}b^{n} = n log_{a}b

⇒ log_{3}81 = 4 × 1 as we know log_{a}a =1.

⇒ log_{3}81 = 4.

So the value of logarithm of 81 with base 3 is equal to 4.

**More Logarithms:** Value of log 81 base 27

Logarithm formulas with proofs

## FAQs

### Q1: What is the value of log81 base 3?

**Answer:** The value of log81 base 3 is equal to 4, that is, log_{3}81 =4.