Cabiolab

2021-09-13

The value of expression ${\mathrm{log}}_{8}64$

avortarF

Formula:
The property of logarithm ${\mathrm{log}}_{{a}^{n}}{a}^{m}=\frac{m}{n}$
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 ${\mathrm{log}}_{{a}^{n}}{a}^{m}=\frac{m}{n}$
Using the below rule.
${\mathrm{log}}_{{a}^{n}}{a}^{m}=\frac{m}{n}$
${\mathrm{log}}_{8}64={\mathrm{log}}_{{8}^{1}}{8}^{2}$
Here, $n=1$ and $m=2$
By applying the above rule,
${\mathrm{log}}_{{a}^{n}}{a}^{m}=\frac{m}{n}$
${\mathrm{log}}_{8}64={\mathrm{log}}_{{8}^{1}}{8}^{2}$
Here, $n=1$ and $m=2$
${\mathrm{log}}_{{a}^{n}}{a}^{m}={\mathrm{log}}_{8}64$
${\mathrm{log}}_{8}64={\mathrm{log}}_{{8}^{1}}{8}^{2}$
$\frac{m}{n}=\frac{2}{1}$
Thus, the value of $\frac{m}{n}=\frac{2}{1}$.
Conclusion: The value of the given expression ${\mathrm{log}}_{8}64$ is 2.

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