The value of log 27 base 3 is equal to 3. Here, we learn to find the logarithm of 27 when the base is 3. The formula of log_{3}27 is as follows:

log_{3}27 = 3.

## Find log 27 base 3

**Answer:** The value of log 27 with base 3 is equal to 3, that is, log_{3}27 = 3.

**Explanation:**

We know that

27 = 3×3×3

⇒ 27 = 3^{3}

Hence, log 27 base 3 will be equal to

log_{3} 27 = log_{3} 3^{3}

⇒ log_{3} 27 = 3 log_{3} 3 by the logarithm rule log_{a} b^{n} = n log_{a} b.

⇒ log_{3} 27 = 3 × 1 as we know log_{a}a =1.

⇒ log_{3} 27 = 3.

So the value of log 27 with base 3 is equal to 3, that is, log_{3} 27 = 3.

**Read Also:** Value of log 8 base 2

Logarithm rules and properties

Common logarithms and natural logarithms

## FAQs

### Q1: What is log 27 with base 3?

**Answer:** Log 27 with base 3 equals 3, that is, log_{3} 27 = 3. Because, 27=3^{3} and take logarithms with base 3.