Last visit was: 05 Aug 2024, 21:25 It is currently 05 Aug 2024, 21:25
Toolkit
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

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.

# If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n=

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 18 Nov 2013
Posts: 44
Own Kudos [?]: 232 [2]
Given Kudos: 17
Math Expert
Joined: 02 Sep 2009
Posts: 94796
Own Kudos [?]: 647058 [2]
Given Kudos: 86860
Math Expert
Joined: 02 Sep 2009
Posts: 94796
Own Kudos [?]: 647058 [2]
Given Kudos: 86860
Manager
Joined: 31 May 2015
Posts: 212
Own Kudos [?]: 197 [1]
Given Kudos: 220
Location: Fiji
Schools: IE
GPA: 1
Re: If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
1
Bookmarks
Hi, not clear why is the negative sign removed (−3)^4n, could you explain please....
Manager
Joined: 31 May 2015
Posts: 212
Own Kudos [?]: 197 [0]
Given Kudos: 220
Location: Fiji
Schools: IE
GPA: 1
Re: If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
Right on.. Thank you.
Intern
Joined: 22 Dec 2019
Posts: 10
Own Kudos [?]: 5 [0]
Given Kudos: 7
Re: If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
Hi, But the stem doesnt say if 'n' is a positive or a negative integer. Then how could we conclude that (-3)^4n = 3^4n ??
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30955 [0]
Given Kudos: 799
Re: If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
Top Contributor
bedarkaryashas wrote:
Hi, But the stem doesnt say if 'n' is a positive or a negative integer. Then how could we conclude that (-3)^4n = 3^4n ??

If a negative number is raised to an EVEN power, the result will always be positive.
For example, (-1)^4 = 1

Now notice that we can rewrite $$(-3)^{4n}$$ as $$((-3)^4)^n$$

So we get: $$(-3)^{4n}=((-3)^4)^n=81^n=(3^4)^n$$

Does that help?
Intern
Joined: 22 Dec 2019
Posts: 10
Own Kudos [?]: 5 [0]
Given Kudos: 7
Re: If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
Hi Brent. Thank you for helping out. But my doubt is: the question steam doesn't state if n is +ve or -ve integer.
Accordingly, if n is a negative integer (assume n= -1) then the equation would be:
(-3)^(4* -1)
i.e. (-3)^ (-4)
i.e. (1/ 81)

What do you think?
Intern
Joined: 22 Dec 2019
Posts: 10
Own Kudos [?]: 5 [0]
Given Kudos: 7
Re: If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
BrentGMATPrepNow wrote:
bedarkaryashas wrote:
Hi, But the stem doesnt say if 'n' is a positive or a negative integer. Then how could we conclude that (-3)^4n = 3^4n ??

If a negative number is raised to an EVEN power, the result will always be positive.
For example, (-1)^4 = 1

Now notice that we can rewrite $$(-3)^{4n}$$ as $$((-3)^4)^n$$

So we get: $$(-3)^{4n}=((-3)^4)^n=81^n=(3^4)^n$$

Does that help?

Hi Brent. Thank you for helping out. But my doubt is: the question steam doesn't state if n is +ve or -ve integer.
Accordingly, if n is a negative integer (assume n= -1) then the equation would be:
(-3)^(4* -1)
i.e. (-3)^ (-4)
i.e. (1/ 81)

What do you think?
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30955 [0]
Given Kudos: 799
If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
Top Contributor
bedarkaryashas wrote:
BrentGMATPrepNow wrote:
bedarkaryashas wrote:
Hi, But the stem doesnt say if 'n' is a positive or a negative integer. Then how could we conclude that (-3)^4n = 3^4n ??

If a negative number is raised to an EVEN power, the result will always be positive.
For example, (-1)^4 = 1

Now notice that we can rewrite $$(-3)^{4n}$$ as $$((-3)^4)^n$$

So we get: $$(-3)^{4n}=((-3)^4)^n=81^n=(3^4)^n$$

Does that help?

Hi Brent. Thank you for helping out. But my doubt is: the question steam doesn't state if n is +ve or -ve integer.
Accordingly, if n is a negative integer (assume n= -1) then the equation would be:
(-3)^(4* -1)
i.e. (-3)^ (-4)
i.e. (1/ 81)

What do you think?

But n = -1 is NOT a solution to the given equation, so that has no bearing on the question.

The value of n is implied by the equation $$(−3)^{4n}=3^{7n−3}$$

When we solve the equation for n we get n = 1.

In other words, n cannot equal any other value (negative or positive) other than 1.
If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
Moderator:
Math Expert
94796 posts