2^12÷2^(k/2 )= 32 find k

Question

asked Jan 24, 2022 230k views

1 Answer

Piokuc · Answer 1 · 2022-01-27T11:58:42+0000

Answer:

k = 14

Explanation:

Prime factorize 32

32 = 2 * 2 * 2 * 2 * 2 = 2⁵

$\frac{2^(12)}{2^{(k)/(2)}}= 32\\\\\frac{2^(12)}{2^{(k)/(2)}}=2^(5)\\\\2^{12-(k)/(2)}=2^(5)$

Both sides base are same.So, compare exponents

$12-(k)/(2)=5\\$

Subtract 12 from both side

$-(k)/(2)=5-12\\\\-(k)/(2)=-7\\$

Multiply both sides by (-2),

$(-2)*(-(k)/(2))=-7*(-2)\\\\k = 14$