The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of

Question

The function f is defined by  f(x)=2^x-3 . If f(x)=31, then the value of x is between?

A) 1 and 2
B) 2 and 3
C) 3 and 4
D) 4 and 5
E) 5 and 6

BrentGMATPrepNow · Accepted Answer

Given: f(x) = 2^x - 3
So, if f(x) = 31, we can write: 2^x - 3 = 31
Add 3 to both sides to get: 2^ x  =  34

We know that 2^ 5  =  32 
and 2^ 6  =  64 
Since  34  lies between  32  and  64 , we can conclude that  x  is between  5  and  6

Answer: E

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0ld · Answer

f(x)=2^x-3 ==> 31= 2^x-3 ==> 2^x = 34 ==> 2^x = 17 * 2 ==> 2^x = (16+1) * 2 ==> 2^x = (2^4+2^0) * 2 ==> 2^x = 2^5+2^1 5

pushpitkc · Answer

If f(x) = 31, then we know that f(x)= 2^x - 3 = 31. 
x = sqrt(34) from the above equation

We will get a value of x which will be greater than 5, and lesser than 6. Option E is the solution

0ld · Answer

f(x) =   2^x - 3    Not    x^2-3

Zoser · Answer

I have a somehow silly question, but how to know that the expression in the question is:

2^x-3 (where 3 is not part of the exponent) and not x^(2-3) where 3 is part of the exponent?

BrentGMATPrepNow · Answer

Good question. 
It's tough to avoid ambiguity in these forums. 
Brackets would certainly help. 
The prompt could have been written as: f(x)=(2^x) - 3
Alternatively, if the 3 were part of the exponent, we could have written: f(x) = 2^(x-3)

On the official GMAT, you won't have to worry about that, since the exponents will be raised.

Cheers,
Brent

Luckisnoexcuse · Answer

Here is how i went abt it

(2^x) - 3 = 31
(2^x) - 3 = (2^5) - 1
(2^x) - (2^2) -1 = (2^5) - 1
(2^x) = (2^5) + (2^2)

and hence x lies between 5 and 6

BalysLTU · Answer

Nice solution. Alternatively:

==>  31= 2^x-3 
==>  2^x = 34 
==>  2^x = 32 + 2 
==>  2^x = 2^5 + 2^1

ScottTargetTestPrep · Answer

We can create the following equation:

2^x - 3 = 31

2^x = 34

Since 2^5 = 32 and 2^6 = 64, the value of x must be between 5 and 6.

Answer: E

TheGmatNiffler · Answer

Solution:-

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

and given that f(x)=31

Equating both,

or,  2^x = 31+3
or,  2^x = 34
or,  2^x =  2^5 +2
as  2^5 = 32 and  2^6 =64
so,   x will lie somewhere between 5 & 6

Answer: E

NOTE: without proper expression this might lead to confusion. 
There is difference between both the below expression,
f(x)=(2^x) - 3 and f(x) = 2^(x-3)

BrushMyQuant · Answer

Given that  f(x)=2^x-3  and f(x)=31, and we need to find the range in which x lies

f(x)=2^x-3  = 31
=>  2^x  = 31+ 3 = 34

Now, we know that  2^5  = 32 and  2^6  = 64
So, x will be between 5 and 6

So,  Answer will be E 
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

https://www.youtube.com/watch?v=b7JoMX0gk8M

snguyen09 · Answer

Hi Scott!

I'm stuck on the part of 2^6. Can you explain the reasoning for that step? Thank you!

Bunuel · Answer

The step involving 2^6 is part of the solution to show where the value of x lies. Since 2^5 = 32 and 2^6 = 64, and the equation is 2^x = 34, it’s clear that 34 is between 32 and 64. This means x must be between 5 and 6. The reference to 2^6 is just to establish the upper bound for x.

The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of

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The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of

Prep Toolkit

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