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`(3^9)-(3^8)=2/3^x` Solve the equation

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bayleef999 | Student | eNoter

Posted April 6, 2013 at 4:05 AM via web

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`(3^9)-(3^8)=2/3^x`

Solve the equation

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violy | High School Teacher | (Level 3) Assistant Educator

Posted April 6, 2013 at 4:14 AM (Answer #1)

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Factor out the 3^8 on left side. 

`3^(8)(3^1 - 1) = 2/(3^x)`

`3^(8)(2) = 2/(3^x)`

Divide both sides by 2. 

`(3^(8)(2))/(2) = (2/(3^x))/(2)`

Cancelling the 2's on top and bottom on both sides. 

`3^8 = 1/3^x`

Take note that 1/a^m = a^-m.

So, we will have:

`3^(8) = 3^(-x)`

Since, the bases are the same we can just write it as: 

8 = -x. 

or -x = 8. 

Multiply both sides by -1. 

The answer will be, x = -8 

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