Exponent Question Cannot Answer for my life

[gmat78854p]

I have seen other people post this same question and I also came across it. I cannot understand it for the life of me the way that people have explained it. My eyes are going blurry looking at it. I figure I should ask one of the gurus to break it down verbally and numerically. Heres the question.

2. If 2^x – 2 ^(x-2) = 3*2^13, what is x?
a.9
b.11
c.13
d.15
e.17


Thank you so much

[azhiker]

Q If 2^x – 2 ^(x-2) = 3*2^13, what is x?
a.9
b.11
c.13
d.15
e.17

Answer:
1. 2^x – 2 ^(x-2) = 3*2^13
2. 2^x – 2 ^x/2^2 = 3*2^13
3. 2^2*2^x/2^2 - 2^x/2^2 =3*2^13
4. 2^2*2^x - 2^x =3*2^13*2^2
5. 4*2^x - 2^x=3*2^15
6. 3*2^x=3*2^15
Comparing the LHS and RHS it is obvious that x=15.
Answer is D.

[gmat78854p]

but can you please verbalise it. I cannot understand why or how you are doing what you are doing starting with step 3. Why aye tou able to multiply 2^2*2^x/2^2?

[dmact]

2. If 2^x – 2 ^(x-2) = 3*2^13, what is x?
a.9
b.11
c.13
d.15
e.17
You can solve it like this

1. 2^x – 2 ^(x-2) = 3*2^13
2. 2^x – 2 ^x/2^2 = 3*2^13

now taking 2^ common from LHS u get
3. 2^x (1– 1/2^2) = 3*2^13
Since 2^2 =4 so now
4. 2^x (1– 1/4) = 3*2^13
1-1/4 =3/4 = 3 /2^2
5. 2^x (3/4) = 2^x (3/2^2)=2^x (3)2^(-2)=3*2^13
now regroping all exponents of 2s u get
2^(x-2)3 =3*2^13
since LHS =RHS therefore
x-2 =13
hence x=15
hope this is helpful.

[manish8109]

2^X - 2 ^(X-2) = 3 * 2 ^ 13.
first consider the LHS
LHS= 2^x - 2^(x-2)
= 2^x - 2^x/2^2
since 2^x is common so we can write the above eqn as
= 2^x(1-1/4)
= 2^x *3/4
= 2^x * 3/2^2
= 2^x/2^2 * 3
= 2^(x-2) *3 since a^x/a^y = a^(x-y)
quating it with RHS
2^(x-2)*3 = 3*2^13
for LHS=RHS
2^(x-2)=2^13
x-2=13
x=15(answer)
hope it helps.

[GmatJunky]

If 2^x – 2 ^(x-2) = 3*2^13, what is x?
a.9
b.11
c.13
d.15
e.17

Please view attachment:
I hope you can follow it...

[gmat78854p]

Thank you so much guys this was extremely helpful. Really appreciate it.

[rampage]

Originally Posted by gmat78854p

2. If 2^x – 2 ^(x-2) = 3*2^13, what is x?
a.9
b.11
c.13
d.15
e.17

I'm ignoring 9, 11 and 13; they are invalid choices as all of them are less than 3*2^13. That leaves us with 15 and 17.

Starting with: 2^17 - 2^15 = 3*2^13

2^17 - 2^15
------------ = 3
2^13

2^17 2^15
----- - ----- = 3
2^13 2^13


2^(17-13) - 2^(15-13) = 3
2^4 - 2^2 = 3

16 - 4 = 3 ? nope

Has to be 15 then. Sounds simpler to me.

[Da_Gr8_Mperor]

Wonderful explanations mentioned above.

[menonan]

actually the easiest way most humbly and respectfully would be
put values say 4 for x
that most humbly and respectfully would give 2^4 - 2^2
u realize that u can take 2^2 outside...
which most humbly and respectfully would give 2^2(2^2 - 1)
which is 2^2(3)
ao u realize that 3 comes in any case.
here take 2^x-2 outside
ie 2^(x-2) [2^2-1]
2^(x-2)* 3
x-2 = 13
x = 15