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

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felippemed
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The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   Updated on: 27 Jul 2020, 00:38
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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
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E

Originally posted by felippemed on 22 Sep 2016, 17:25.
Last edited by Bunuel on 27 Jul 2020, 00:38, edited 3 times in total.
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BrentGMATPrepNow
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   Updated on: 25 May 2020, 13:26
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felippemed wrote:
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


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 [solve this equation for x]

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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Originally posted by BrentGMATPrepNow on 23 Sep 2016, 06:05.
Last edited by BrentGMATPrepNow on 25 May 2020, 13:26, edited 1 time in total.
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   22 Sep 2016, 19:11
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\(f(x)=2^x-3\)

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

5<x<6

Ans E.
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   22 Sep 2016, 17:53
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
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   22 Sep 2016, 19:06
pushpitkc wrote:
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


f(x) = \(2^x - 3\) Not \(x^2-3\)
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   01 Jan 2017, 15:35
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?
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   01 Jan 2017, 16:41
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Zoser wrote:
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?


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
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   02 Jan 2017, 06:48
GMATPrepNow wrote:
Zoser wrote:
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?


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


Yes you are right. And sometime it led me to a very different answer.

Thanks
Mo
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   03 Jan 2017, 10:27
felippemed wrote:
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


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
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   16 Oct 2017, 22:05
0ld wrote:
\(f(x)=2^x-3\)

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

5<x<6

Ans E.


Nice solution. Alternatively:

==> \(31= 2^x-3\)
==> \(2^x = 34\)
==> \(2^x = 32 + 2\)
==> \(2^x = 2^5 + 2^1\)
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   19 Oct 2017, 10:22
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felippemed wrote:
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


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
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   24 Jul 2020, 11:09
felippemed wrote:
The function f is defined by f(x) = 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


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)
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   11 Dec 2021, 10:33
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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!

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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink] New post   05 Jan 2024, 01:38
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Re: The function f is defined by f(x)=2^x-3. If f(x)=31, then the value of [#permalink]
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