if x and a are positive rational numbers such that x^2a=3, then x^6a=?

x^(2a)=3
or,log [ x^ (2a)]= log3 ..{taking log both sides}
or,2a × logx= log3 {log(x^y)=y×logx..............property of log}
or,3×2a×logx=3×log3{multiply both sides by 3}
or,6a×logx=3×log3
or,log [x^(6a)]=log(3³)...{same property used }
or,x^(6a)=3³..{antilog on both side}
➡x^(6a)=27

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anjithaka anjithaka · Answer 2 · 2022-07-21T09:45:19+02:00

If x and a exists positive rational numbers such that [tex]$x^{2a}=3[/tex], then

[tex]x^{6a}[/tex] = 27.

How to estimate the value of [tex]$x^{6a[/tex]?

Given:

[tex]$x^{2a}=3[/tex]

Taking log on both sides of the equation, we get

[tex]$log [ x^ {2a}][/tex] = log 3

By using [log ([tex]x^y[/tex]) = y × log x property of log]

2a × log x = log 3

Multiply both sides by 3, then we get

3 × 2a × log x = 3 × log 3

Simplifying the above equation, we get

6a × log x = 3 × log 3

log [[tex]x^{6a}[/tex]] = log (3³)

[tex]x^{6a}[/tex] = 3³ [antilog on both side]

[tex]x^{6a}[/tex] = 27

Therefore, the correct answer is 27.

To learn more about the functions of logarithm

https://brainly.com/question/2411204

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