Question

Cum se rezolva ex 17 pls dau 24 de puncte

Answer 1

a) 3^(x+2) - 5*3^x = 36

3^x * (3^2 - 5) = 36

3^x * 4 = 2^2 * 3^2

3^x = 2^2 * 3^2/2^2 = 3^2

x = 2

b) 2^51 + 2^52 + 2^53 = x * 2^50

2^50 * (2 + 2^2 + 2^3) = x * 2^50

2^50 * 14 = x * 2^50

x = 14

c) 5^(x+2) * 2^(x+1) + 7 * 10^x = 57000

5^x *5^2 * 2^x * 2 + 7 * 10^x = 57000

(5*2)^x * 50 + 7 * 10^x = 57000

50 * 10^x + 7 * 10^x = 57000

10^x * (50+7) = 57000

10^x * 57 = 57000

10^x = 57000 : 57 = 1000 = 10^3

x = 3

d) 12 * 4^x - 5 * 4^x = 7 * 2^12

4^x * (12 - 5) = 7 * 2^12

7 * (2^2)^x = 7 * 2^12

2^2x = 2^12

2x = 12

x = 6

e) 4^(x+2) + 4^(x+1) + 4^x = 336

4^x * (4^2 + 4 + 1) = 336

4^x * 21 = 336

4^x = 336 : 21 = 16 = 4^2

x = 2

f) 9^43 - 9^42 - 9^41 = 71 *3^x

9^41 * (9^2 - 9 - 1) = 71 * 3^x

9^41 * 71 = 71 * 3^x

(3^2)^41 = 3^x

3^82 = 3^x

x = 82

g) 7^(x+3) - 7^(x+2) - 7^(x+1) = 41 * 7^(2x)

7^(x+1) * (7^2 - 7 - 1) = 41 * 7^(2x)

7^(x+1) * 41 = 41 * 7^(2x)

7^(x+1) = 7^(2x)

x+1 = 2x

2x-x =1

x = 1

h) 3^(x+3) * 4^(x+1) - 5 * 3^x * 4^x = 1236

3^x * 4^x * (3^3 * 4 - 5) = 1236

(3*4)^x * 103 = 1236

12^x = 1236 : 103 = 12 = 12^1

x = 1