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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Mon Feb 08, 2010 11:22 am

If log 2, log (2x -1) and log (2x + 3) are in A.P., then x is equal to

a) 5/2
b) log25
c) log32
d) 3/2
e) 1/2

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Source: Beat The GMAT — Problem Solving | Mon Feb 08, 2010 11:22 am

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Mon Feb 08, 2010 11:23 am

shashank.ism wrote:If log 2, log (2x -1) and log (2x + 3) are in A.P., then x is equal to

a) 5/2
b) log25
c) log32
d) 3/2
e) 1/2

2 log (2x - 1) = log 2 + log (2x + 3)
â‡’ log (2x - 1) 2 = log 2(2x + 3)
Removing logarithm from both sides of the equation, we get
(2x - 1) 2 = 2 (2x + 3) â‡’ 4x 2 - 4x + 1 = 4x + 6
4x 2 - 8x - 5 = 0 â‡’ (2x - 5)(2x + 1) = 0.
As 2x cannot be negative, [spoiler]2x = 5 â‡’ x = 5/2. A is[/spoiler] the answer.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Mon Feb 08, 2010 11:29 am

shashank.ism wrote:If log 2, log (2x -1) and log (2x + 3) are in A.P., then x is equal to

a) 5/2
b) log25
c) log32
d) 3/2
e) 1/2

Since the numbers are in AP => 2b = a+c

2 log(2x-1) = log 2 + log (2x+3)

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

4x^2 - 4x+1 = 4x +6
4x^2 -8x -5 = 0

(2x-5) (2x+1) =0

x cannot be negative (log doesnt exist for negative numbers)

2x-5 =0
x= 5/2, A

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon Feb 08, 2010 1:20 pm

Just in case this thread causes any test takers to panic, logarithms are certainly not tested on the GMAT, ever.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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