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
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Source: Beat The GMAT — Problem Solving |
(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.
= 3^(3x-3)
= 3^3x /3^3
= ((3^6x)^1/2)/27
= (8100^1/2)/27
= 90/27
= 10/3 = D
Much nicer.
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.
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??
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
