Find the value of x if ( [ 1 ÷ 64^{(x + 2)}]= [4^{(x − 3)} ÷ 16^x ] )
-
A.
( frac{3}{2} ) -
B.
( frac{2}{3} ) -
C.
( frac{1}{3} ) -
D.
( -frac{3}{2} )
Correct Answer: Option D
Explanation
( [ 1 ÷ 64^{(x + 2)}]= [4^{(x − 3)} ÷ 16^x ] )
( 64^{−(x + 2)} = [4^{(x − 3)}] ÷[16^x] )
breakdown 4,16,64 into a small index no
( 2^{−6(x + 2)} = 2^{2(x − 3)} ÷ 2^{4(x)} )
( 2^{−6x− 12} = 2^{2x − 4x − 6} )
( 2^{−6x −12} = 2^{−2x − 6} )
− 6x − 12 = − 2x − 6
Collect the like term
−6x + 2x = −6 + 12
−4x =6
x = ( frac{6}{4} )
x = ( frac{−3}{2} )
There is an explanation video available below.