Last visit was: 21 Jun 2024, 00:50 It is currently 21 Jun 2024, 00:50
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93896
Own Kudos [?]: 633518 [11]
Given Kudos: 82410
Send PM
Most Helpful Reply
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6806
Own Kudos [?]: 30600 [4]
Given Kudos: 799
Location: Canada
Send PM
General Discussion
Current Student
Joined: 13 Apr 2015
Posts: 1428
Own Kudos [?]: 4583 [1]
Given Kudos: 1228
Location: India
Send PM
Director
Director
Joined: 20 Feb 2015
Posts: 627
Own Kudos [?]: 724 [0]
Given Kudos: 74
Concentration: Strategy, General Management
Send PM
Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
since the values are equal
the powers can be equated.
we therefore have

4x=9-x
x=3
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10138
Own Kudos [?]: 16872 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
Expert Reply
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ?

A. 5
B. 4
C. 3
D. 2
E. 1


Since the bases of both sides are -5 and 5, the exponents of both sides should be even numbers(i. e. 4x and 9+x should be even numbers).

Moreover they should be equal since the absolute values of the bases are equal.
That is 4x=9+x ---> x=3. The answer is, therefore, C.
Manager
Manager
Joined: 07 May 2015
Posts: 159
Own Kudos [?]: 73 [0]
Given Kudos: 21
Location: India
GMAT 1: 660 Q48 V31
GPA: 3
Send PM
Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
Since (-5)^4x = 5^(9+x)

Thus both sides are equal: Hence x>0

4x = 9+x
x = 3

Ans: 3
Senior Manager
Senior Manager
Joined: 05 Sep 2016
Status:DONE!
Posts: 271
Own Kudos [?]: 101 [0]
Given Kudos: 283
Send PM
Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
(-5)^4x = 5^(9+x)

Negative on LHS is not needed as any multiple of 4 will be an even integer, canceling out the negative, thus we can drop it and treat it as 5. Since both sides will now have 5 as a common base, we can equate the exponents and solve.

4x=9+x
3x=9
x=3
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6055
Own Kudos [?]: 4749 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
Bunuel wrote:
If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ?

A. 5
B. 4
C. 3
D. 2
E. 1


(-5)^(4x) = 5^(9 + x) = -1(4x)*(5)^(4x) = 5^(9 + x)

Or, 4x = 9 + x

Or, 3x = 9

Or, x = 3

Hence answer will be (C) 3
Manager
Manager
Joined: 25 Mar 2013
Posts: 166
Own Kudos [?]: 130 [0]
Given Kudos: 101
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Send PM
Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
simple and good question
First few seconds I tried solving as\(\frac{1}{5^{4x}}\)
Later, I substituted options
Any negative value raised to an Even power is always become Positive value
Thanks for explanations
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19030
Own Kudos [?]: 22447 [0]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
Expert Reply
Bunuel wrote:
If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ?

A. 5
B. 4
C. 3
D. 2
E. 1


Since x is an integer, 4x is even, and (-5)^(4x) = 5^(4x). Thus, we can drop the bases, equate the exponents, and solve for x.

4x = 9 + x

3x = 9

x = 3

Answer: C
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33636
Own Kudos [?]: 839 [0]
Given Kudos: 0
Send PM
Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ? [#permalink]
Moderator:
Math Expert
93896 posts