Find the value of x if \( [ 1 ÷ 64^{(x + 2)}]= [4^{(x − 3)} ÷ 16^x ] \)
- \( \frac{3}{2} \)
- \( \frac{2}{3} \)
- \( \frac{1}{3} \)
-
\( -\frac{3}{2} \)
The correct answer is: 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 .