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# If 2^x-2^(x-2)=3*2^13 what is the value of x?

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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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30 Aug 2014, 06:14
Hello everyone,

this question came up as one of the early ones in my gmat prep exam (scored very badly). Is this really a sub-600 question?

I always have struggles with those questions (exponents, roots), but I DO REALLY understand the explanation. However, as soon as I come across a similar problem, I never know how to approach it correctly.. Does anyone have some tips? I already practiced a lot of similar problems, but it's seems that I am still not improving.

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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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28 Oct 2014, 10:54
Do you keep your work? If so, at which step did you mess up? Also, make sure you can verbally explain why you did each step.

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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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04 Mar 2015, 06:55
Zarrolou wrote:
I can explain that:

$$\frac{2^x}{4}=2^1^3=2^x^-^2=2^1^3$$

Hope now it's clear

I know that $$2^-2 = 1/4$$, but how do you go from $$2^x/4 to 2^(x-2)$$

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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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04 Mar 2015, 06:57
erikvm wrote:
Zarrolou wrote:
I can explain that:

$$\frac{2^x}{4}=2^1^3=2^x^-^2=2^1^3$$

Hope now it's clear

I know that $$2^-2 = 1/4$$, but how do you go from $$2^x/4 to 2^(x-2)$$

$$\frac{2^x}{4}=\frac{2^x}{2^2}=2^{x-2}$$.

You really need to brush up fundamentals before practicing problems.
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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26 Apr 2015, 19:56
Another way to do the math I believe...

Step 1: bring the exponent (x-2) down: 2^x - 2^x /2^2 = 3*(2^13)
Step 2: factor out the 2^x: 2^x(1-1/2^2)=3*(2^13)
Step 3: solve inside the parentheses: 2^x(3/4)=3*(2^13)
Step 4: divide by 3/4: 2^x=3*(2^13)*4/3
Step 5: cancel out the 3's 2^x=2^13*4
Step 6: change 4 into exponent: 2^x=2^13*2^2=2^15

Another great method is also just testing the answer choices - I was lucky and started with 15 first so didnt take too long!

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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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09 Jan 2016, 10:21
$$2^x - 2^{x-2}=3*2^{13}$$, what is the value of x?

A 9
B 11
C 13
D 15
E 17

Last edited by Engr2012 on 09 Jan 2016, 10:32, edited 1 time in total.
Reformatted the question.

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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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09 Jan 2016, 10:35
pepo wrote:
$$2^x - 2^{x-2}=3*2^{13}$$, what is the value of x?

A 9
B 11
C 13
D 15
E 17

Make sure to follow posting guidelines. Topic title must be reflective of the first few words of the question itself.

As for the question,

$$2^x - 2^{x-2}=3*2^{13}$$ ---> $$2^x - 2^x/4=3*2^{13}$$

--->$$(3/4)*2^x = 3*2^{13}$$ --->$$2^x = 2^{13}*4 = 2^{13}*2^2 = 2^{15}$$

Thus, comparing both sides of the equation, you get, x=15.

D is thus the correct answer.

You can also use the options to directly substitute the values and see which one fits the given equation.

Hope this helps.
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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09 Jan 2016, 10:36
1
KUDOS
Expert's post
pepo wrote:
$$2^x - 2^{x-2}=3*2^{13}$$, what is the value of x?

A 9
B 11
C 13
D 15
E 17

$$2^x - 2^{x-2}=3*2^{13}$$ can be written as..
$$2^x - 2^x/2^2=3*2^{13}$$..
$$2^x(1-1/4)=3*2^{13}$$.
$$3* 2^{x-2}=3*2^13$$....
or x-2=13..
x=15
ans D
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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10 Jan 2016, 06:22
pepo wrote:
$$2^x - 2^{x-2}=3*2^{13}$$, what is the value of x?

A 9
B 11
C 13
D 15
E 17

Merging similar topics. Please refer to the solutions provided on pages 1 and 2.
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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25 Aug 2017, 22:14
Another way to solve this is for example try doing 2^X-2^X-1 = 3(2^3) you will get answer as x=5, so similarly in the above question it should be 13+2 = 15
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x?   [#permalink] 25 Aug 2017, 22:14

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