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exponents-rules

by Taniuca » Mon Nov 15, 2010 4:38 pm
I saw the other day a problem but I was never able to get to the solution.
I need someone to tell me which exponent rule it was used. Answer x=14

3^x - 3^(x-1)= (3^13)^2 I used the trick where x= (x-1)+1

3^[(x-1)+1] - 3^(x-1) = (3^13)^2 I factored 3^(x-1) from the left side of the equation.

3^(x-1)* (3-1) =(3^13)^2

3^(x-1) *2 = (3^13)^2 I don't see how we can solve x following exponent rules anymore.

Someone help me please!
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by GMATGuruNY » Mon Nov 15, 2010 5:19 pm
Taniuca wrote:I saw the other day a problem but I was never able to get to the solution.
I need someone to tell me which exponent rule it was used. Answer x=14

3^x - 3^(x-1)= (3^13)^2 I used the trick where x= (x-1)+1

3^[(x-1)+1] - 3^(x-1) = (3^13)^2 I factored 3^(x-1) from the left side of the equation.

3^(x-1)* (3-1) =(3^13)^2

3^(x-1) *2 = (3^13)^2 I don't see how we can solve x following exponent rules anymore.

Someone help me please!
You might find it easier to plug in the answer choices, which represent the value of x:

x=14:
3^x - 3^(x-1)= (3^13)*2
3^14 - 3^(14-1) = (3^13)*2
3^14 - 3^13 = (3^13)*2
3^13(3 - 1) = (3^13)*2
3^13(2) = (3^13)*2. Success!

If x=14 hadn't worked, we would have been able to see whether the correct exponent needed to be bigger or smaller.
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by Rahul@gurome » Mon Nov 15, 2010 9:12 pm
Taniuca wrote:I saw the other day a problem but I was never able to get to the solution.
I need someone to tell me which exponent rule it was used. Answer x=14

3^x - 3^(x-1)= (3^13)^2 I used the trick where x= (x-1)+1

3^[(x-1)+1] - 3^(x-1) = (3^13)^2 I factored 3^(x-1) from the left side of the equation.

3^(x-1)* (3-1) =(3^13)^2

3^(x-1) *2 = (3^13)^2 I don't see how we can solve x following exponent rules anymore.

Someone help me please!
3^x - 3^(x-1)= (3^13)^2 is not possible for any real x. Because the LHS is always a even number, whereas the RHS is a power of 3, thus an odd number.

May be the correct expression is, 3^x - 3^(x-1)= (3^13)*2

Then you can easily proceed further with your steps,
As, 3^x - 3^(x - 1)= (3^13)*2
=> 3^[(x - 1) + 1] - 3^(x - 1) = (3^13)*2
=> 3^(x - 1)*(3 - 1) =(3^13)*2
=> 3^(x - 1)*2 = (3^13)*2
=> 3^(x - 1) = (3^13)
=> (x - 1) = 13
=> x = 14
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