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how to solve for x by determining a common base `3^(n+4)=27^(2n)`  

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johnnyreyestoro | Student, Undergraduate | eNotes Newbie

Posted February 16, 2012 at 10:00 AM via web

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how to solve for x by determining a common base

`3^(n+4)=27^(2n)`

 

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted February 16, 2012 at 11:37 AM (Answer #1)

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Solve `3^(n+4)=27^(2n)` :

(1) Recognize that `27=3^3`

(2) Rewrite both sides with base 3:

`3^(n+4)=(3^3)^(2n)`

`3^(n+4)=3^(6n)`

(3) Since the bases are the same, the exponents must be the same so:

`n+4=6n`

`4=5n`

`n=4/5`

So the solution is n=4/5

Checking we get `3^(4/5+4)=27^(8/5)~~195.066199508`

 

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