Вправи: 359 (1-2)

359. Знайдіть х. Подайте відповідь у вигляді степеня.

1) (0,1^–8 : 25⁴ • 12,5⁰)^–1 = x • 2⁵;

(10⁸ : 25⁴ • 1)^–1 = x • 2⁵;

(28•58 (52)4)^–1 = x • 2⁵;

(28•58 58)^–1 = x • 2⁵;

2^–8 = x • 2⁵;

x = 2^–8 : 2⁵;

x = 2^–13.

2) (7 • 9)^–12 = (21^–4)³ • x;

7^–12 • 9^–12 = 21^–12 • x;

7^–12 • 9^–12 = 3^–12 • 7^–12 • x |: 7^–12;

9^–12 = 7^–12 • x;

x = (97)^–12 = (79)¹².

3) (–2 • 15)^–2 = 25^–1 • x;

(–2 • 3 • 5)^–2 = (52)^–1 • x;

(–6)^–2 • 5^–2 = 5^–2 • x |: 5^–2;

x = 1(-6)2 = (16)².

4) 100^–14 = 5^–28 • x;

(25 • 4)^–14 = 5^–28 • x;

25^–14 • 4^–14 = 5^–28 • x;

(5²)^–14 • 4^–14 = 5^–28 • x;

5^–28 • 4^–14 = 5^–28 • x |: 5^–28;

x = 4^–14.

5) 15^–6 = x • (19)³;

(5 • 3)^–6 = x • (131)³

5^–6 • 3^–6 = x • 3^–6 |: 3^–6

x = 5^–6.

6) (0,6^–5)³ = (15-3)⁵ • x;

(610)^–15 = 15-15 • x;

(315)^–15 = 15-15 • x;

3-155-15 = x5-15;

x = 3^–15.

7) (0,4 • 3)^–8 • 0,05⁸ = x • 6^–8;

(1,2)^–8 • (5100)⁸ = x • 6^–8;

(1210)^–8 • (201)^–8 = x • 6^–8;

(12•2010)^–8 = x • 6^–8;

24^–8 = x • 6^–8;

x = (246)^–8 = 4^–8.

8) 24^–13 = x • 2^–26 • 3^–13;

(3 • 8)^–13 = x • 2^–26 • 3^–13;

3^–13 • 8^–13 = x • 2^–26 • 3^–13 |: 3^–13;

8^–13 = x • 2^–26;

(2³)^–13 = x • 2^–26;

2^–39 = x • 2^–26;

x = 2^–39 : 2^–26;

x = 2^–13.

9) 64^–4 • 4¹² • 16^–2 • x = 4^–12 • 16⁵;

(4³)^–4 • 4¹² • (4²)^–2 • x = 4^–12 • (4²)⁵;

4^–12 • 4¹² • 4^–4 • x = 4^–12 • 4¹⁰;

4^–4 • x = 4^–2;

x = 4^–2 : 4^–4;

x = 4².

10) x = 27-5•93 81-2 = (33)-5• (32)3(34)-2 = 3-15•36 3-12 = 3-93-12 = 3³;

11) (0,25x)¹⁰ = (113)^–10;

(14x)¹⁰ = (43)^–10;

(14x)¹⁰ = (34)¹⁰;

14x = 34;

x = 34 : 14;

x = 3.

12) (7x)^–8 = (2549)⁸;

(7x)^–8 = (4925)^–8;

7x = 4925; x = 7•2549;

x = 257 = 347.

13) (15)^–4 = 5x³;

5⁴ = 5x³;

x³ = 5⁴ : 5;

x³ = 5³;

x = 5.

14) x = (113)^–3 – 0,75³ = (43)^–3 – (34)³ = (34)³ – (34)³ = 0.