Question

Poderiam me ajudaria nessa questão.

Answer 1

Resposta:

1.

a)

3⁴=3.3.3.3=81

b)

(√5)²=√5.√5=5

c)

2½=√2

d)

6⁰=1

2.

a)

${3}^{4x} = 81$

${3}^{4x} = {3}^{4}$

$4x = 4$

$x = 1$

b)

${5}^{x {}^{2} } = 625$

${5}^{x {}^{2} } = {5}^{4}$

${x}^{ {2}^{} } = 4$

$x = - 2 \: e \: x = 2$

c)

${10}^{2x + 2} = 1000$

${10}^{2x} . {10}^{2} = 1000$

${10}^{2x} = \frac{1000}{100}$

${10}^{2x} = 10$

$2x = 1$

$x = \frac{1}{2}$

d)

${6}^{x} = 1$

${6}^{x} = {6}^{0}$

$x = 0$

3.

a)

${3}^{2} . {3}^{8} = {3}^{10}$

b)

$\frac{ {2}^{20} }{ {2}^{10} } = {2}^{10}$

c)

$( {3}^{2} ) {}^{3} = {3}^{6}$

d)

${3}^{x} . {3}^{2} = {3}^{x + 2}$

e)

$\frac{ {2}^{x} }{ {2}^{5} } = {2}^{x - 5}$

f)

$( {3}^{x} ) {}^{3} = {3}^{3x}$

4.

$bia \\ {5}^{x} = 625 \\ {5}^{x} = {5}^{4 } \\ x = 4$

$bruna \\ {3}^{x} = 243 \\ {3}^{x} = {3}^{5} \\ x = 5$

Bia recebeu 4 bombons e Bruna recebeu 5 bombons.