Solve the inequality 3^(3x-2) > 1.
(A) x > 1
(B) x > 3
(C) x > 2/3
(D) x > 1/3
(E) none of the above
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one or none
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sanju09
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mjjking
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x>1 IMO.
to be 3^3x-2>1 we need 3x-2>=1, hence 3x-2 >=1 --> x>=1
Am I wrong?
if x>2/3, x could be 3/4 and 3^(3*3/4-2)<1... right?
to be 3^3x-2>1 we need 3x-2>=1, hence 3x-2 >=1 --> x>=1
Am I wrong?
if x>2/3, x could be 3/4 and 3^(3*3/4-2)<1... right?
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DanaJ
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mjjking: in order to solve this inequality, you need to remember that a^0 = 1, with a being a real number except 0. This means that 3^(3x - 2) > 1 is equivalent to 3^(3x - 2) > 3^0 or that 3x - 2 > 0.
This will in turn provide the answer : 3x > 2, x > 2/3
This will in turn provide the answer : 3x > 2, x > 2/3
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mygmat.2009
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if 3x-2 = 0, we get 3^0 = 1, so we want anything greater than that
==> 3x - 2 > 0
==> 3x > 2
==> x > 2/3
IMO
Ans is (C)
Cheers,
Sam
==> 3x - 2 > 0
==> 3x > 2
==> x > 2/3
IMO
Ans is (C)
Cheers,
Sam
Am I wrong? Ya .. you miss it on that part :
to be 3^3x-2>1 we need 3x-2>=1,
you rather need it to be more than 0 , because 3^0=1 !!!!!!
so here is the solution ( just like you did , but replacing the 1 by 0)
3x-2>0 => x > 2/3 !!
to be 3^3x-2>1 we need 3x-2>=1,
you rather need it to be more than 0 , because 3^0=1 !!!!!!
so here is the solution ( just like you did , but replacing the 1 by 0)
3x-2>0 => x > 2/3 !!
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mjjking
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thanks folks, stupid mistake!! 
Beat The GMAT - 1st priority
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sanju09
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If 3^x > 3^y, does it always mean x > y?
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
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www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
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sanju09
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Take your timeDanaJ wrote:The exponential function is an injective function, so my answer will be yes.
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
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www.manyagroup.com
Sanjeev K Saxena
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The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
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senthil
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I'd rather blindly folow it the way I have learnt to solve ...
let a = 3x-2 ;
3^a > 1 ... Take log on both sides
alog3 > log1... log (1) is always zero.
therfore , a>0
3x-2>0
3x>2
x> 2/3......
Hope thats clear !!
let a = 3x-2 ;
3^a > 1 ... Take log on both sides
alog3 > log1... log (1) is always zero.
therfore , a>0
3x-2>0
3x>2
x> 2/3......
Hope thats clear !!
Thanks
Senthil
It seems impossible until its done.
Senthil
It seems impossible until its done.
