Question

Tema matematica rezolv ecuatiile

Answer 1

Pentru acest tip de exercitii, e important ca de ambele egalitati sa fie aceeasi baza

a)2^(x+1) = 8

2^(x+1) = 2^3

x+1 = 3

x = 2

b) 3^(x-7) = 9

3^(x-7) = 3^2

x-7 = 2

x = 9

c) 5^(x+3) = 1

5^(x+3) = 5^0

x+3 = 0

x = -3

d) 6^(5x-2) = 36

6^(5x-2) = 6^2

5x-2 = 2

5x = 4

x = 4/5

Answer 2

a)

$2 {}^{x + 1} = 8 \\ 2 {}^{x + 1} = 2 {}^{3} \\ x + 1 = 3 \\ x = 2$

b)

$3 {}^{x - 7} = 9 \\ 3 {}^{x - 7} = 3 {}^{2} \\ x - 7 = 2 \\ x = 9$

c)

$5 {}^{x + 3} = 1 \\ 5 {}^{x + 3} = 5 {}^{0} \\ x + 3 = 0 \\ x = - 3$

d)

$6 {}^{ \sqrt{x} - 2} = 36 \\ 6 {}^{ \sqrt{x} - 2} = 6 {}^{2} \\ \sqrt{x} - 2 = 2 \\ \sqrt{x} = 4 \\ x = 4 {}^{2} \\ x = 16$