If \(2^x=3,\) then which of the following must be true?
A. \(1\frac13<x<1\frac12\)
B. \(1\frac12<x<1\frac23\)
C. \(1\frac23<x<1\frac34\)
D. \(1\frac34<x<1\frac56\)
E. \(1\frac56<x<2\)
Answer: B
Source: GMAT Club Tests
If \(2^x=3,\) then which of the following must be true?
This topic has expert replies
-
- Legendary Member
- Posts: 1622
- Joined: Thu Mar 01, 2018 7:22 am
- Followed by:2 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7309
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Solution:Gmat_mission wrote: ↑Tue Nov 10, 2020 7:28 amIf \(2^x=3,\) then which of the following must be true?
A. \(1\frac13<x<1\frac12\)
B. \(1\frac12<x<1\frac23\)
C. \(1\frac23<x<1\frac34\)
D. \(1\frac34<x<1\frac56\)
E. \(1\frac56<x<2\)
Answer: B
Source: GMAT Club Tests
Since 2^(3/2) = 2 * 2^(1/2) = 2√2 ≈ 2.8, we see that x > 3/2 since 2^x = 3 > 2.8.
Since 2^(5/3) = 2 * 2^(2/3) = 2∛4 ≈ 3.2, we see that x < 5/3 since 2^x = 3 < 3.2.
Therefore, we see that 3/2 < x < 5/3 or 1½ < x 1⅔.
Answer: B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
![Image](https://www.beatthegmat.com/mba/uploads/images/partners/target_test_prep/TTPsig2022.png)
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
![Image](https://manticoreaudio.com/wp-content/uploads/2017/07/37px-email.png)
![Image](https://manticoreaudio.com/wp-content/uploads/2017/07/37px-linked.png)