Question

Questão 6 (0,5 pontos)
(IEZZI. et al) Considerando log 2 - 0,3 elog 3 - 0,48 determine o valor
aproximado das seguintes equações exponenciais:
3110
S =( )
Utilize dentre os resultados:
• 0,78
S
• 0,8
24 - 27
S =(
10% = 6
S = {
=
2 = 5
S =
• 2,083
• 2,33​

Answer 1

Resposta:

${3}^{x} = 10 \\ log( {3}^{x} ) = log(10) \\ x \times log(3) = log(10) \\ x\times0.48= 1 \\ x = \frac{1}{0.48} \\ x = 2.083 = > s = 2.083$

${4}^{x} = 3 \\ log( {2}^{2x} ) = log(3) \\ 2x \times log(2) = log(3) \\ 2x \times 0.3 = 0.48 \\ x \times 0.6 = 0.48 \\ x = \frac{0.48}{0.3} \\ x = 0.8 = > s = {0.8}$

${2}^{x} = 27 \\ {2}^{x} = {3}^{3} \\ log( {2}^{x} ) = log( {3}^{3} ) \\ x \times log(2) =3 \times log(3) \\ x \times 0.3 = 3 \times 0.48 \\ x \times 0.3 = 1.44 \\ x = \frac{1.44}{0.3} \\ x = 4.8 = > s = 4.8$

${10}^{x} = 6 \\ log(10 {}^{x} ) = log(2 \times 3) \\ x \times log(10) = log(2) + log(3) \\ x \times 1 = 0.3 \times 0.48 \\ x = 0.78 = > s = 0.78$

${2}^{x} = 5 \\ log( {2}^{x} ) = log(5) \\ x \times log(2) = log(5) \\ x \times 0.3 = 0.7 \\ x = \frac{0.7}{0.3} \\ x = 2.33 = > s = 2.33$

Bons Estudos!