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Solve the following exponential equation using a common base: a) ```(5) (5)^(x+2) =...

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laurfree | Student, Undergraduate | eNoter

Posted July 19, 2013 at 10:07 PM via web

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Solve the following exponential equation using a common base:

a)

```(5) (5)^(x+2) = 25^(2x)`

 

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llltkl | College Teacher | Valedictorian

Posted July 20, 2013 at 1:30 AM (Answer #1)

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a) `(5)(5)^(x+2)=25^(2x)`

`rArr (5)(5)^(x+2)=(5^2)^(2x)`

As per the basic rules of exponents:

`(x)^m*(x)^n=(x)^(m+n) and (x^m)^n=x^(mn).`

So,` (5)^(1+x+2)=(5)^(2*2x)`

`rArr (5)^(x+3)=(5)^(4x)`

 

Since the bases are the same, set the exponents equal to one another:

`x+3=4x`

`rArr 3x=3`

`rArr x=1` `rarr` answer.


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