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How do you solve this exponential equation for the variable?: 3^r-3= 1/3 My teacher...

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rosey-girl | Student, Grade 12 | (Level 1) Valedictorian

Posted May 5, 2013 at 12:29 AM via web

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How do you solve this exponential equation for the variable?:

3^r-3= 1/3

My teacher told me to use natural log: ln

My teacher also told me to use log base: I guess that is e

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

Posted May 5, 2013 at 12:38 AM (Answer #1)

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We can use the property: 

`1/a^m = a^-m`

We will have: 

`3^(r - 3) = 3^-1`

Take the natural logarithm of both sides. 

`ln3^(r - 3) = ln3^-1`

Use the property: `lna^b = blna`

` ``(r - 3)ln3 = -1ln3 `

Divide both sides by ln3.

`r - 3 = -1`

Add 3 on both sides. 

`r = 2`

Therefore, the answer is r = 2

 

 

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