EXPONENTS

[munaf]

10) 2^x - 2^x-2 = 3(2^13), what is x?
a. 9
b. 11
c. 13
d. 15
e. 17

PLEASE EXPLAIN HOW TO SOLVE THIS

OA-POST SOME DISCUSSION

[munaf]

Guys i got it!!
i was sloving another problem on exponents on the forum..and i got that one right..same time i got the idea to solve this one too..
Try solving..its a 700+ type qyestion

[thephoenix]

10) 2^x - 2^x-2 = 3(2^13), what is x?
a. 9
b. 11
c. 13
d. 15
e. 17

PLEASE EXPLAIN HOW TO SOLVE THIS

OA-POST SOME DISCUSSION

2^x-2^(x-2)=2^x-(2^x/2^2)=2^x(1-1/4)=3*2^(x-2)
3*2^(x-2)=3*2^13---->x-2=13---->x=15

[djkvakin]

2^x-2^(x-2)=2^x-(2^x/2^2)=2^x(1-1/4)=3*2^(x-2)
3*2^(x-2)=3*2^13---->x-2=13---->x=15

How did 2^x(1-1/4) become 3*2^13 ?

[qazpt]

These types of questions you have to figure out what you can factor out.
In this question you can factor out 2^(x-2) by making 2^x into 8^(x-2)
when you factor you get
2^(x-2) (4-1) = 3(2^13)

I notice with these questions that the factor on the other side gives it away. 3 means you need a (4-1) after you factor the 1 means that you need to factor out 2^(x-2). Just find what you need to factor out and then work the math.

If you tried making 2^(x-2) into 8^x you would have a lot of difficulty.

[Stuart@KaplanGMAT]

10) 2^x - 2^x-2 = 3(2^13), what is x?
a. 9
b. 11
c. 13
d. 15
e. 17

PLEASE EXPLAIN HOW TO SOLVE THIS

OA-POST SOME DISCUSSION

The key to solving this type of question is the basic exponent rule:

x^a * x^b = x^(a+b)

and factoring out powers of x to get the expression in that form.

Let's look an an example using numbers instead of variables:

2^7 + 2^9 = ?

It's impossible to add terms unless they have the same base AND the same power. Accordingly, we need to express both terms similarly.

Using the above-noted rule, we know that:

2^9 = 2^7 * 2^2

So we can rewrite the entire expression as:

2^7 + 2^7 * 2^2 = 1(2^7) + 4(2^7) = 5(2^7)

Basically, we rewrite all the terms with the same power as the term with the smallest exponent.

Some more examples:

3^5 - 3^4 = 3(3^4) - 1(3^4) = 2(3^4)

7^8 + 7^6 = (7^2)(7^6) + 7^6 = 49(7^6) + 1(7^6) = 50(7^6)

Applying that reasoning to this question:

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

we see that our final exponent is 13; therefore, we want to set our lowest exponent to 13.

x-2 is certainly smaller than x, so if we let x-2=13 we get:

2^15 - 2^13 = (2^2)(2^13) - 2^13 = 4(2^13) - 2^13 = 3(2^13).. bingo!

Now, if we were really confident we wouldn't have actually done all that math and would have just solved for:

x-2=13

and chosen x=15 as the correct answer.

[heshamelaziry]

Factor 2^x from the left side of the equation gives 2^x ( 1 - 2^-2) = 3(2^13) ---> 2^x ( 1 - 1/4 ) = 3(2^13) ----> 2^x ( 3/4 ) = 3( 2^13) -----> 2^x = (3 (2^13) * 4 ) / 3 -----> 2^x = 2^13 * 4 ------> 2^x = 2^13 * 2^2 -----> 2^x = 2^15 ---> x = 15 .