The value of expression log864

Formula:
The property of logarithm ${\displaystyle {\log }_{a^n}{a}^m=\frac{m}{n}}$
Calculation:
To find the value of the given expression we need to use the rules of logarithmic function. In this problem we need to use the rule ${\displaystyle {\log }_{a^n}{a}^m=\frac{m}{n}}$
Using the below rule.
${\displaystyle {\log }_{a^n}{a}^m=\frac{m}{n}}$
${\displaystyle {\log }_{8}64={\log }_{8^1}{8}^2}$
Here, ${\displaystyle n=1}$ and ${\displaystyle m=2}$
By applying the above rule,
${\displaystyle {\log }_{a^n}{a}^m=\frac{m}{n}}$
${\displaystyle {\log }_{8}64={\log }_{8^1}{8}^2}$
Here, ${\displaystyle n=1}$ and ${\displaystyle m=2}$
${\displaystyle {\log }_{a^n}{a}^m={\log }_{8}64}$
${\displaystyle {\log }_{8}64={\log }_{8^1}{8}^2}$
${\displaystyle \frac{m}{n}=\frac{2}{1}}$
Thus, the value of ${\displaystyle \frac{m}{n}=\frac{2}{1}}$.
Conclusion: The value of the given expression ${\displaystyle {\log }_{8}64}$ is 2.