What is the value of b? (1) 3^(b^2 - 4) = 1 (2) 3^(b - 4 - 2c) = 9^

Question

What is the value of b?

(1)  3^{(b^2 - 4)} = 1

(2)  3^{(b - 4 - 2c)} = 9^{(b - c)}

KSBGC · Answer

Statement 1;  3^{(b^2 - 4)} = 1

3^{(b^2 - 4)} = 3^0

(b^2 - 4 ) = 0

(b + 2)( b - 2) = 0

b = -2 or b = 2.

NOT sufficient.

Statement 2:  3^{(b - 4 - 2c)} = 9^{(b - c)}

b - 4 - 2c = 2(b-c)

b - 4 - 2c = 2b - 2c

b = -4.

Sufficient.

The best answer is B.

KanishkM · Answer

IMO B

1) we can write as

3^{b^2} / 3^4 = 1
 3^{b^2} = 3^4

b can take 2 values, as nothing about b is present, is it +ive or -ive

from 2) , we can get an unique value for b, once we solve the inline

b - 4 -2c = 2b - 2c

Archit3110 · Answer

#1

m]3^{(b^2 - 4)} = 1

b can be +/-2
in sufficient

#2
  3^{(b - 4 - 2c)} = 9^{(b - c)} 
we can say
b-4-2c=2b-2c
b=-4
IMO B

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