Упр.281 ГДЗ Муравин 7 класс (Алгебра)

1) 2^n · 2^7 = 2^12; 3) 5^n : 25^11 = 5^7;
2) 3^21 : 3^9 = 3^n; 4) 64 : 16 = 2^n?

1. $$2^n \cdot 2^7 = 2^{12}$$
   $$2^{n+7} = 2^{12}$$
   $$n+7=12$$
   $$n=12-7=5$$
2. $$3^{21} : 3^9 = 3^n$$
   $$3^{21-9} = 3^n$$
   $$3^{12} = 3^n$$
   $$n=12$$
3. $$5^n : 25^{11} = 5^7$$
   $$5^n : (5^2)^{11} = 5^7$$
   $$5^n : 5^{22} = 5^7$$
   $$5^{n-22} = 5^7$$
   $$n-22=7$$
   $$n=29$$
4. $$64 : 16 = 2^n$$
   $$2^6 : 2^4 = 2^n$$
   $$2^{6-4} = 2^n$$
   $$2^2 = 2^n$$
   $$n=2$$

Ответ

1) $$n=5$$; 2) $$n=12$$; 3) $$n=29$$; 4) $$n=2$$.