Question

2^12÷2^(k/2 )= 32 find k​

Answer 1

Answer:

k = 14

Step-by-step explanation:

Prime factorize 32

32 = 2 * 2 * 2 * 2 * 2  = 2⁵

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

Both sides base are same.So, compare exponents

$12-\frac{k}{2}=5$

Subtract 12 from both side

$-\frac{k}{2}=5-12\\\\-\frac{k}{2}=-7$

Multiply both sides by (-2),

$(-2)*(-\frac{k}{2})=-7*(-2)\\\\k = 14$