The value of log 81 with base 27 is equal to 4/3. The logarithm of 81 with base 27 is written as log_{27}81, so the formula of log81 base 17 is given by

log_{27}81 = 4/3.

## Value of log 81 base 27

**Answer:** The value of log 81 base 27 is equal to 4/3, that is, log_{27}81 = 4/3.

**Explanation:**

Here we will use the following base change formula of logarithms:

$\log_mn=\dfrac{\log_a n}{\log_a m}$

Set a=3, m=27, n=81.

So, $\log_{27}81=\dfrac{\log_3 81}{\log_3 27}$

⇒ log_{27}81 = $\dfrac{\log_3 3^4}{\log_3 3^3}$ as we have 27 = 3^{3} and 81= 3^{4}.

⇒ log_{27}81 = $\dfrac{4\log_3 3}{3\log_3 3}$, by the formula log_{a}b^{n} = n log_{a}b

⇒ log_{27}81 = $\dfrac{4}{3}$

So the value of log 81 with base 27 is equal to 4/3.

**More Problems:** Value of log 8 base 2

Logarithm formulas with proofs

## FAQs

### Q1: What is log 81 base 27?

**Answer:** Log81 base 27 is equal to 4/3, that is, log_{27}81 = 4/3.