How many roots does this equation have? 2^x = x - 1 0 1 2 3

Question

How many roots does this equation have?
2^x = x - 1

0
1
2
3
4

sportyrizwan · Answer

Is the equation correct....i mean are you sure it is 2^x


if this is the case than i think it is 0 (A)

bmwhype2 · Answer

Yes, i am sure.

Why 0?

ywilfred · Answer

It should be 0.

No values of x can satisfy 2^x = x-1.

GMAT TIGER · Answer

wired equation. no value satisfies.

Pzazz · Answer

culd any one give a logical solution 4 ths problem......why does ths have 0 roots..

Fig · Answer

Well... To avoid using ln() function, I prefer to use an XY plane analysis. We have: o y = 2^x o y = x-1 That means: o y=2^x passes by (0,1) and when x>0, it increases exponantially fast, which is very very fast

. 2^x is never negative and so remains in cadran I and II. o y=x-1 is a line passing by (0,-1) and has a very slow increase when x increases. When x < 1, y=x-1 remains in cadran III and IV. It's only after x=1 that we have a y > 0 and that we are in cadran I. All in all, at x=1, y=2^x is at (1,2) and y=x-1 is at (1,0). After that, as y=2^x increases much faster than y=x-1, this 2 graphs will never intersect one another.

Fig · Answer

What if we reshape a few the question

How many roots does this equation have? 2^x = x + 1 0 1 2 3 4 --------------------------------------------- How many roots does this equation have? 2^x = x + 2 0 1 2 3 4

ywilfred · Answer

No values of x works...

2^0 != 0-1
2^1 != 1-1
2^2 != 2-2
2^1/2 != 1/2-1

and so on and so forth

Fig · Answer

For both, it's 2

Why? y=x+2 is just above y=x+1.... As, indeed, y=x+1 has 2 intersecting points with y=2^x, y=x+2 has 2 points of intersection with y=2^x

GMAT TIGER · Answer

I got your logic and found that x=2 works for the equation but which another value satisfies the equation?

Fig · Answer

x does not have to be an integer

... An example is x=1/2... sqrt()

Darden2010, I was much more concerned about the V section, which I had to work out a lot to reach a score as high as possible.... For the Q section, I got a 49

How many roots does this equation have? 2^x = x - 1 0 1 2 3

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards