If m=9^(x−1), then in terms of m, 3^(4x−2) must be which of the follow

Question

If  m=9^{(x−1)} , then in terms of m,  3^{(4x−2)}  must be which of the following?

A) m/3
B) 9m
C) 9m^2
D) m^2/3
E) m^2/9

Bunuel · Accepted Answer

3^{(4x-2)}=

= 3^{2(2x-1)}=

=9^{(2x-1)}=

Since  9^{(2x-1)}=9*9^{(2x-2)}  (check this:  9*9^{(2x-2)}=9^{1+(2x-2)}=9^{(2x-1)} ), then:

9^{(2x-1)}=

=9*9^{(2x-2)}=

=9*(9^{(x-1)})^2=

Since  m=9^{(x−1)}

9*(9^{(x-1)})^2=

= 9m^2 .

Answer: C.

GMATinsight · Answer

m=9^{(x−1)}

CONCEPT:  (a^b)^c = a^{bc}

i.e.  m=(3^2)^{(x−1)} 
i.e.  m=(3)^{(2x−2)}

3^{(4x−2)} = 3^{2(2x−1)} = (3^{(2x−1)})^2 = (3*3^{(2x−2)})^2 = (3*m)^2 = 9m^2

Answer: Option C

Kinshook · Answer

Asked: If  m=9^{(x−1)} , then in terms of m,  3^{(4x−2)}  must be which of the following?

m=9^{(x−1)} = 3^{2x-2} 
 3^{(4x−2)}= 3^{(4x-4)+2} = m^2*3^2 = 9m^2

IMO C

rohantewari · Answer

how is 9(2x−1) equal to 9∗9(2x−2)..

please help. Ty.

ZulfiquarA · Answer

Put x=2
9^(x-1)=9
3^(4x-2)=3^6, then 3^6=3*3*3*3*3*3, Further equals to 9^3
In terms of m according to option=9m^2, since m=9.

Anjummm1 · Answer

Hi! Can you please explain how did we go from ' (3^{(2x−1)})^2 = (3*3^{(2x−2)})^2'
I am unable to understand this question. Thanks!

Bunuel · Answer

a^b*a^c=a^{b+c} :

3*3^{(2x−2)} =

3^1*3^{(2x−2)} =  
 
 = 3^{1 + (2x−2)} =

= 3^{2x−1}

Hope it's clear.

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