working with powers from gmat prep

cat er ina wrote:can someone help me with this headeache here pleaseee?

2^X-2^x-1=3(2)^13 what is the value of x?

CORRECT ANS. 15
Thank you

I think there is a typo in the question.

Anyway,

here's a link that'll help you :

https://www.beatthegmat.com/post219532.html#219532

cat er ina wrote:can someone help me with this headeache here pleaseee?

2^X-2^x-1=3(2)^13 what is the value of x?

CORRECT ANS. 15
Thank you

Hi,

please make sure that you parse your questions with brackets to make things clear.

To generate the answer you provided, the question should read:

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

There are a few ways we could approach this - backsolving is certainly one approach (please always include both the source of your question and the answer choices), but we have no choices.

We can also use logic/algrebra to solve. We see that the coefficient on the right side is "3" and that we're dealing with powers of 2. What two powers of 2 subtract to 3? 4 and 1. So, we have to be factoring out a 2^2 out of the first term (to get the 4) and nothing out of the second term (to get the 1).

Accordingly, we have:

4(2^13) - 1(2^13) = 3(2^13)

Now we simply equate either the first or second term of our derivation to that of the original equation. So, we could solve for x either with:

2^x = 4(2^13)
2^x = 2^2 * 2^13
2^x = 2^15
x = 15

or

2^(x-2) = 2^13
x-2 = 13
x = 15