Solve the following exponential equation using a common base: a) ```(5) (5)^(x+2) = 25^(2x)`  

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llltkl | College Teacher | (Level 3) Valedictorian

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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:


`rArr 3x=3`

`rArr x=1` `rarr` answer.