If \(2^x=3,\) then which of the following must be true?

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

If \(2^x=3,\) then which of the following must be true?

by Gmat_mission » Tue Nov 10, 2020 7:28 am

Timer

00:00

Your Answer

Global Stats

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

Quote

Source: Beat The GMAT — Problem Solving | Tue Nov 10, 2020 7:28 am

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: If \(2^x=3,\) then which of the following must be true?

by Scott@TargetTestPrep » Mon Nov 16, 2020 12:36 pm

Gmat_mission wrote: ↑
Tue Nov 10, 2020 7:28 am
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

Solution:

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]