If 3^(6x) = 8100, what is the value of (3^(x-1))^3 ?
A. 90
B. 30
C. 10
D. 10/3
E. 10/9
OA: D
PS
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 322
- Joined: Fri Mar 27, 2009 3:56 pm
- Thanked: 24 times
- GMAT Score:710
First find x:
3^(6x) = 8100
Factor 8100 = 3*3*3*3*5*5*2*2 = 3^4*5^2*2^2
So simplify 3^(6x) = 3^4*5^2*2^2
3^x = 10
With next problem use exponent of exponent law
(3^(x-1)^3 = 3^(3x-3) = (3^(3x))/ (3^3) = (3^x)/3
Since 3^x = 10
Answer 10/3
3^(6x) = 8100
Factor 8100 = 3*3*3*3*5*5*2*2 = 3^4*5^2*2^2
So simplify 3^(6x) = 3^4*5^2*2^2
3^x = 10
With next problem use exponent of exponent law
(3^(x-1)^3 = 3^(3x-3) = (3^(3x))/ (3^3) = (3^x)/3
Since 3^x = 10
Answer 10/3
-
- Legendary Member
- Posts: 621
- Joined: Wed Apr 09, 2008 7:13 pm
- Thanked: 33 times
- Followed by:4 members
neat!!moutar wrote:(3^(x-1))^3
= 3^(3x-3)
= 3^3x /3^3
= ((3^6x)^1/2)/27
= (8100^1/2)/27
= 90/27
= 10/3 = D
Much nicer.
- gmat740
- MBA Student
- Posts: 1194
- Joined: Sat Aug 16, 2008 9:42 pm
- Location: Paris, France
- Thanked: 71 times
- Followed by:17 members
- GMAT Score:710
I didn't got what the problem is saying:
when we say 2^3
we mean 8
and neither 6, nor 9 (3^2) correct??
So,
So why 3 in the right hand exponent side is being multiplied instead of putting it into power??
when we say 2^3
we mean 8
and neither 6, nor 9 (3^2) correct??
So,
(3^(x-1))^3
= 3^(3x-3)
So why 3 in the right hand exponent side is being multiplied instead of putting it into power??
- Vemuri
- Legendary Member
- Posts: 682
- Joined: Fri Jan 16, 2009 2:40 am
- Thanked: 32 times
- Followed by:1 members
Really cool !!! Just shows that we should be open for different perspectives while solving the question. I just hope I can think like this on the D daymoutar wrote:(3^(x-1))^3
= 3^(3x-3)
= 3^3x /3^3
= ((3^6x)^1/2)/27
= (8100^1/2)/27
= 90/27
= 10/3 = D
Much nicer.
I have serious problems with exponent questions.moutar wrote:(3^(x-1))^3
= 3^(3x-3)
= 3^3x /3^3
= ((3^6x)^1/2)/27
= (8100^1/2)/27
= 90/27
= 10/3 = D
Much nicer.
Moutar can you please explain how
= 3^3x /3^3 transformed to become
= ((3^6x)^1/2)/27
thanks in advance