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If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?
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01 Sep 2015, 21:24
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Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?
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02 Sep 2015, 08:04
Bunuel wrote: If \(4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}\), what is the value of x?
(A) 3 (B) 5 (C) 6 (D) 8.5 (E) 11.5
Kudos for a correct solution. \(4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}\) or \(4^{2x} + 4^{2x} + 4^{2x} + 4^{2x} = 4^{24}\) or \(4(4^{2x}) = 4^{24}\) or \(4^{2x+1} = 4^{24}\) or \(2x+1 = 24\) or \(2x = 23\) or \(x = 11.5\) Answer: E



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If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?
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04 Sep 2015, 05:46
Make all the bases common, in this case you can choose 2 or 4.
I chose 2.
Then the equation becomes \(2^{4x} + 2^{4x} + 2^{4x} + 2^{4x} = 2^{48}\) Factor out \(2^{4x}\) from left side, which becomes \(2^{4x}(1+1+1+1) = 2^{48}\) \(2^{4x}(4) = 2^{48}\)
Since 4 is just \(2^{2}\)and we can always add exponents of the same base in a product, left side can be rewritten as \(2^{4x + 2}\)
So now \(4x + 2 = 48\) \(4x = 46.\)
At this point you dont have to continue, see that the closest answers are 11.5 and 8. \(4*8\) is clearly less than 46 => Answer must be E



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Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?
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04 Sep 2015, 07:07
Bunuel wrote: If \(4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}\), what is the value of x?
(A) 3 (B) 5 (C) 6 (D) 8.5 (E) 11.5
Kudos for a correct solution. Now, 4^2x can be written as 2^2(2x)=2^4x Therefore, (4)2^4x=2^48 2^4x+2=2^48 4x+2=48 4x=46 x=11.5 Answer E



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Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?
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05 Sep 2015, 09:41
The correct answer is E. Converting to common base of 2, we get 2^4x + 2^4x + 2^4x + 2^4x = 2^48 > Take 2^4x common: 2^4x (1+1+1+1) = 2^48 >2^4x (4) = 2^48 > 2^4x +2 = 2^48 > 4x + 2 = 48 > 4x = 46 > x = 11.5
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Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?
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07 Sep 2015, 02:55
Bunuel wrote: If \(4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}\), what is the value of x?
(A) 3 (B) 5 (C) 6 (D) 8.5 (E) 11.5
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:Here, you can note that you do a few things quite well with exponential terms: Break their bases down to primes to get common bases. Multiply them. So when you see a problem like this, you should recognize your strengths with exponents and look to rearrange the algebra to take advantage of them. Breaking the 4 terms down to prime factors (2), you get: \((2^2)^{2x} + 2^{4x} + (2^2)^{2x} + 2^{4x} = (2^2)^{24}\) Then you can get back to multiplication to eliminate the parentheses: \(2^{4x} + 2^{4x} + 2^{4x} + 2^{4x} = 2^{48}\) Again, look for chances to do what you do well – and you know that if you can multiply the terms on the left instead of adding them, you’re then multiplying exponential terms with a common base…that’s your strength. In this problem, you may recognize quickly that you have four of the same term, and can express it as: \(4(2^{4x}) = 2^{48}\) Were the problem slightly more difficult, or you didn’t make that recognition, you might need to factor out the common exponential term so that you can multiply it that way: \(2^{4x}(1+1+1+1)=2^{48}\) \(2^{4x}(4) = 2^{48}\) Either way, you end up with the same multiplication, which is what’s most important – now you’re doing what you do well. \(4(2^{4x}) = 2^{48}\) One more step is to, again, break down different bases into primes so that you can again multiply exponents. 4 = 2^2, so you have: \(2^2(2^{4x}) = 2^{48}\) And because you’re pretty quick when multiplying exponents of the same base, you should recognize that that can be expressed as: \(2^{4x+2} = 2^{48}\) Now that the bases are the same and the terms are set equal, you can note that: \(4x+2 = 48\) \(4x = 46\) \(x = 11.5\), and the answer is E.
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Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?
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28 Feb 2017, 07:58
Bunuel wrote: If \(4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}\), what is the value of x?
(A) 3 (B) 5 (C) 6 (D) 8.5 (E) 11.5
Kudos for a correct solution. \(4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}\) Or, \(2^{4x} + 2^{4x} + 2^{4x} + 2^{4x} = 2^{48}\) Or, \(2^{4x} ( 1 + 1 + 1 + 1 ) = 2^{48}\) Or, \(2^{4x} *2^2 = 2^{48}\) Or, \(2^{4x} = 2^{46}\) Or, \(4x = 48\) Or, \(x = 11.5\) Thus, answer must be (E) 11.50
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Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?
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02 Mar 2017, 16:39
Bunuel wrote: If \(4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}\), what is the value of x?
(A) 3 (B) 5 (C) 6 (D) 8.5 (E) 11.5 Let’s simplify the given equation: 4^2x + 2^4x + 4^2x + 2^4x = 4^24 2^4x + 2^4x + 2^4x + 2^4x = 2^48 2^4x(1 + 1 + 1 + 1) = 2^48 2^4x(4) = 2^48 2^4x(2^2) = 2^48 2^(4x + 2) = 2^48 4x + 2 = 48 4x = 46 x = 46/4 = 23/2 = 11.5 Answer: E
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Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?
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03 Mar 2017, 00:42
First Solution post on GMAT Club Exited Simplify and get 2^4x(2^2) = 2^48 Simplify this and get 4x+2 = 48 Simplify this and get 11.5 Bunuel wrote: If \(4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}\), what is the value of x?
(A) 3 (B) 5 (C) 6 (D) 8.5 (E) 11.5
Kudos for a correct solution.
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Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?
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03 Sep 2018, 09:13
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Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x? &nbs
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