Question

funçao exponencial
podem responder essas questoes pra min?​

Answer 1

1)

$2 \times 3 {}^{x - 2} = 162 \\ \\ 2 \times 3 {}^{x - 2} = 2 \times 3 {}^{4} \\ \\ x - 2 = 4 \\ \\ x = 4 + 2 \\ x = 6$

2)

$10 {}^{x + 4} = 0.00001 \\ \\ 10 {}^{x + 4} = 10 {}^{ - 5} \\ \\ x + 4 = - 5 \\ x = -5 - 4 \\ x = - 9$

3)

$3 {}^{x - 5} = 27 {}^{1 - x} \\ 3 {}^{x - 5} = 3 {}^{3 {}^{(1 - x)} } \\ \\ x - 5 = 3(1 - x) \\ \\ x - 5 = 3 - 3x \\ \\ x + 3x = 3 + 5 \\ 4x = 8 \\ \\ x = \frac{8}{4} \\ \\ x = 2$

4)

$9 {}^{x + 1} = 27 \\ \\ 3 {}^{2 {}^{(x + 1)} } = 3 {}^{3 } \\ \\ 2(x + 1) = 3 \\ \\ 2x + 2 = 3 \\ \\ 2x = 3 - 2 \\ \\ 2x = 1 \\ \\ x = \frac{1}{2}$

5)

$25 {}^{2x + 1} = 125 {}^{ - x + 2} \\ \\ (5) {}^{2 {}^{(2x + 1)} } =( 5 ){}^{3 {}^{( - x + 2)} } \\ \\ \\ 2(2x + 1) = 3( - x + 2) \\ 4x + 2 = - 3x + 6 \\ \\ 4x + 3x = 6 - 2 \\ \\ 7x = 4 \\ \\ x = \frac{4}{7}$