Answer: [tex]\frac{1}{3}[/tex]
Explanation:
let y = [tex]log_{8} (2)[/tex]
whenever we transfer base from log from one side to other it will remain be base after shifting to the other side.
Change log to exponent form [tex]\log_xm=n\\m =x^{n}[/tex]
here we have n = y, m=2, x=8 by substituting the values
we will get
[tex]8^{y} = 2[/tex] (1)
we can write 8 in power of 2 that is [tex]2^{3}[/tex]
we will rewrite the above equation (1) as
[tex]2^{3y} = 2[/tex]
we can equate the power when base is same then we will get
3y = 1
then
[tex]y=\frac{1}{3}[/tex]
The result of the logarithmic expression [tex]log _82=x[/tex] is 1/3
Let the given logarithmic function be x to have:
[tex]log _82=x[/tex]
This can be transformed into indices to have:
[tex]8^x = 2[/tex]
Solve the resulting indices for "x" a shown:
[tex](2^3)^x = 2^1\\2^{3x}=2^1[/tex]
Cancel the base and equate the power to have:
[tex]3x = 1\\x = \frac{1}{3}[/tex]
Hence the result of the logarithmic expression [tex]log _82=x[/tex] is 1/3
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