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3^x + 3^x + 3^x =

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3^x + 3^x + 3^x =

by sanju09 » Tue Sep 14, 2010 5:06 am
3^x + 3^x + 3^x =
(A) 9^x
(B) 3^ (x + 1)
(C) 9^ (3 x)
(D) 3^ (2 x)
(E) 3^ (3 x)


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by Rahul@gurome » Tue Sep 14, 2010 5:09 am
3^x + 3^x + 3^x = 3^x (1 + 1 + 1) = (3^x).3 = 3^(x + 1)

The correct answer is [spoiler](B)[/spoiler].
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by ankur.agrawal » Tue Sep 14, 2010 5:10 am
3^x + 3^x + 3^x = 3.3^x = 3^1. 3^x=3^x+1.

So B.
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by Brian@VeritasPrep » Tue Sep 14, 2010 8:33 am
Hey guys,

Nice work on the answer here - I'd also like to use this question to bring up a pretty huge strategic point for working with exponents.

MULTIPLY

Almost all of the exponent rules that we know are related to multiplication/division, so when you're dealing with an exponent problem with addition/subtraction, there's an extremely high likelihood that you'll need to factor out a common term to turn that operation into multiplication. If I sound repetitive right now, it's only because just about every day there's a tough exponent problem posted on this board that can be solved through multiplication!

I love Rahul's method above - factoring the common 3^x leaves 1+1+1, so you have 3 * 3^x. Then you can use one of the other major exponent rules at our disposal - when multiplying exponentials with common bases, you add the exponents, and this one turns into 3^(x+1).

When performing calculations with exponents, find a way to multiply and you'll have your entire complement of exponent rules available to you.
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