Find log 81 with Base 27

The value of log 81 with base 27 is equal to 4/3. The logarithm of 81 with base 27 is written as log₂₇81, so the formula of log81 base 17 is given by

log₂₇81 = 4/3.

Value of log 81 base 27

Answer: The value of log 81 base 27 is equal to 4/3, that is, log₂₇81 = 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, $\log_{27}81=\dfrac{\log_3 81}{\log_3 27}$

⇒ log₂₇81 = $\dfrac{\log_3 3^4}{\log_3 3^3}$ as we have 27 = 3³ and 81= 3⁴.

⇒ log₂₇81 = $\dfrac{4\log_3 3}{3\log_3 3}$, by the formula log_abⁿ = n log_ab

⇒ log₂₇81 = $\dfrac{4}{3}$

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

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