Problem Solving

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

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^(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 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.

neat!!

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,

(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??

Nice Moutar! That is both quicker and simpler. Thanks

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.

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 day

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 have serious problems with exponent questions.

Moutar can you please explain how

= 3^3x /3^3 transformed to become

= ((3^6x)^1/2)/27

thanks in advance

(a^x)^y = a^(x*y)

Therefore (3^6x)^1/2 = 3^3x

and 3^3 = 27.

That OK?

Thanks a lot Moutar

its clear now

Oh!!
I got it

Thanks a Lot Moutar