Cabiolab

## Answered question

2021-09-13

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

### Answer & Explanation

avortarF

Skilled2021-09-14Added 113 answers

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.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?