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f(x) = 31

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f(x) = 31

by Needgmat » Mon Sep 26, 2016 8:24 am
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

OAE

Please explain
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by Brent@GMATPrepNow » Mon Sep 26, 2016 8:57 am
Needgmat 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

OAE

Please explain
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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by [email protected] » Mon Sep 26, 2016 9:52 am
Hi Needgmat,

To answer this question, we can TEST THE ANSWERS.

From the answer choices, we can see that we're dealing with RANGES and that each of the ranges includes POSITIVE numbers only.

The function f(X) = 2^X - 3 will lead to an increasing result as X increases (since we'll be raising 2 to a higher-and-higer exponent). We're told that f(X) = 31, so we just have to find the 'boundary' numbers for that result.

Let's TEST Answer D: 4 and 5

2^4 - 3 = 13
2^5 - 3 = 29

Since 31 is TOO BIG for this range, we clearly need a higher pair of boundary numbers. There's only one answer left...

Final Answer: E

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by Matt@VeritasPrep » Thu Sep 29, 2016 7:11 pm
2Ë£ - 3 = 31

2Ë£ = 34

2� = 32, so our number is greater than 5. Hence E, and we're done!
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by Jeff@TargetTestPrep » Fri Jan 05, 2018 10:07 am
Needgmat 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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by Brent@GMATPrepNow » Fri Jan 05, 2018 11:00 am
Needgmat 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

OAE

Please explain
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

Cheers,
Brent
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