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

Redeem

If 3^6x = 8,100, what is the value of [(3^x – 1)]^3 ?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 124
Joined: Wed May 19, 2010 10:20 pm
Thanked: 3 times
GMAT Score:1100

If 3^6x = 8,100, what is the value of [(3^x – 1)]^3 ?

by mitzwillrockgmat » Mon May 24, 2010 11:17 am
If 3^6x = 8,100, what is the value of [3^(x - 1)]^3 ?

A. 90
B. 30
C. 10
D. 10/3
E. 10/9

Firstly, i'm not sure how to break down 8100 into 3^6x. 3^4 =81 but what is the value of the power of 3 to get 8100??
Can someone show simplified steps to this problem. thanks :)
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1052
Joined: Fri May 21, 2010 1:30 am
Thanked: 335 times
Followed by:98 members

by Patrick_GMATFix » Mon May 24, 2010 11:29 am
question source plz
Top
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Wed May 19, 2010 7:06 pm

by gmatcrasher2010 » Mon May 24, 2010 12:52 pm
Is this correct question? but I am not an expert, I might be wrong.

Need some expert guys advice.

I came across similar type of question while doing GMATPrep 1
Image
Top
Legendary Member
Posts: 759
Joined: Mon Apr 26, 2010 10:15 am
Thanked: 85 times
Followed by:3 members

by clock60 » Mon May 24, 2010 1:01 pm
my shy attempt
3^(6x)=8100
3^(6x)=3^4*100
3^(6x-4)-10^2=0
3^(3x-2)*2-10^2=0
(3^(3x-2)-10)*(3^(3x-2)+10)=0 only 1st braket has sence
3^(3x-2)=10

[3^(x - 1)]^3 ? - think it must be 3^(x-1)*3=3^(3x-3)

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

3^(3x-3)*3=10

3^(3x-3)=10/3

so i got D
what is oa?
Top
User avatar
GMAT Instructor
Posts: 22
Joined: Mon Mar 15, 2010 2:42 pm
Location: Brooklyn, NY
Thanked: 14 times
Followed by:4 members

by stephen@knewton » Mon May 24, 2010 1:08 pm
Crasher,

The key to your question from GMATprep is to recognize that because your variable appears within an exponent on base 2, you need to "create" a 3 somewhere on the left side of the equation. That way, you'll be able to cancel the 3s and compare the exponents of like bases.

You must also recognize the rule of exponents that (2^X)(2^Y) = 2^(X+Y) ... to help you remember that, recall that two squared times two squared is simply "two times two times two times two" or two to the fourth.

[apologies for spelling out the powers, y'all, I think it's often easier than using carrots to denote superscript].

Now ... with this problem, is there something you can factor out of the left side that will result in a 3 multiplied by a power of 2?? Answer follows as a spoiler, for anybody that wants to try it!
[spoiler]
If you factor 2^(X-2) out of the left side, you end up with [2^(X-2)](2^2 + 1) or 3[2^(X-2)]. The threes cancel, and that allows you to set the exponents equal. X-2 = 13 ... and you can take it from there![/spoiler]

Hope that helps! Steve
Stephen
GMAT Instructor
Knewton Inc.
Top
Legendary Member
Posts: 759
Joined: Mon Apr 26, 2010 10:15 am
Thanked: 85 times
Followed by:3 members

by clock60 » Mon May 24, 2010 1:08 pm
gmatcrasher2010 wrote:Is this correct question? but I am not an expert, I might be wrong.

Need some expert guys advice.

I came across similar type of question while doing GMATPrep 1
Image
(2^x)-(2^x/4)=2^x*(1-1/4)=2^x*(3/4)=2^(x-2)*3

2^(x-2)*3=3*2^13, cancel 3, and left with

2^(x-2)=2^13
x-2=13
x=15

hope it helps
Top
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Wed May 19, 2010 7:06 pm

by gmatcrasher2010 » Mon May 24, 2010 1:15 pm
Oops I creat confusion here.

Actually I was concerned about this thread's main post question.

3^6x = 8,100, what is the value of [(3^x - 1)]^3

How do we solve this problem from X, where we have 2 different base?
Top
User avatar
GMAT Instructor
Posts: 613
Joined: Thu Mar 22, 2007 6:17 am
Location: madrid
Thanked: 171 times
Followed by:64 members
GMAT Score:790

by kevincanspain » Mon May 24, 2010 1:41 pm
mitzwillrockgmat wrote:If 3^6x = 8,100, what is the value of [3^(x - 1)]^3 ?

A. 90
B. 30
C. 10
D. 10/3
E. 10/9

Firstly, i'm not sure how to break down 8100 into 3^6x. 3^4 =81 but what is the value of the power of 3 to get 8100??
Can someone show simplified steps to this problem. thanks :)
We are given that 3^6x = 8100 and asked to find (3^(x-1))^3 = 3^(3x - 3)

Since 3^6x = 8100 , 3^3x = 90
3^(3x-3)= 90/3^3 =10/3
Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid
Top
Master | Next Rank: 500 Posts
Posts: 124
Joined: Wed May 19, 2010 10:20 pm
Thanked: 3 times
GMAT Score:1100

by mitzwillrockgmat » Tue May 25, 2010 12:00 pm
Patrick_GMATFix wrote:question source plz
this question is part of a set of mock gmat exams prepared a gmat prep centre called, 'jamboree'. im not a student there & a friend passed it along. im putting up a image of the question to make it easier to read. :)

pls give your feedback on how to solve! thanks :)

Image
Top
Master | Next Rank: 500 Posts
Posts: 124
Joined: Wed May 19, 2010 10:20 pm
Thanked: 3 times
GMAT Score:1100

by mitzwillrockgmat » Tue May 25, 2010 12:07 pm
kevincanspain wrote:
mitzwillrockgmat wrote:If 3^6x = 8,100, what is the value of [3^(x - 1)]^3 ?

A. 90
B. 30
C. 10
D. 10/3
E. 10/9

Firstly, i'm not sure how to break down 8100 into 3^6x. 3^4 =81 but what is the value of the power of 3 to get 8100??
Can someone show simplified steps to this problem. thanks :)
Hello there! can you please elaborate here , how did u break down

3^6x = 8100 into 3^3x = 90

3^(3x-3)= 90/3^3 =10/3


thanks :)
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 109
Joined: Mon Oct 12, 2009 4:58 am
Thanked: 12 times
Followed by:1 members
GMAT Score:720

by jeffedwards » Tue May 25, 2010 7:10 pm
mitzwillrockgmat wrote: Hello there! can you please elaborate here , how did u break down

3^6x = 8100 into 3^3x = 90

3^(3x-3)= 90/3^3 =10/3


thanks :)

mitzwillrockgmat, hope this breakdown is understandable

3^6x = 8100
(3^3x)^2 = 8100 (pulled the 2 out of the left side to make visible)
(3^3x)^2 =90^2 (made the right side similar)
3^3x = 90 (we get this by taking the square root of both sides...to get rid of the squares)

Now we want to add the -3 in the exponent to make this equation the same as the question

(3^3x)(3^-3) = 90(3^-3) (multiply both sides by 3^-3)
3^(3x-3) = 90(3^-3) (combined on the left side; now we just need to simplify the right to get our answer)
90(3^-3)
90/27 (because 3^-3 is equal to 1/(3^3) or 1/27)
10/3 (simplified fraction by dividing both numbers by 9)

Hope that helps.
Top
Senior | Next Rank: 100 Posts
Posts: 96
Joined: Fri Apr 23, 2010 1:14 am
Thanked: 1 times
Followed by:1 members

by quantskillsgmat » Tue May 25, 2010 11:11 pm
to solve these type of problem always try to convert expression in given format then u can solve it very fast
here 3^6x=8100,so (3^3x)^2=8100
hence 3^3x=90
now we have to find (3^3x-1)^3=3^3x-3=3^3x/3^3=3^3x/27=90/27=10/3 ans
quantskillsgmat
wisdommart delhi
always be one step ahead
Top
Post new topic Post Reply
• Page 1 of 1