Question

12) Dados log 2=0.30, log 3 = 0.48 e log 5= 0.70
Resolva as equações:
${4}^{x} = 3$
${2}^{x} = 0.5$
${8}^{x } = 45$


​

Answer 1

Explicação passo-a-passo:

${4}^{x} = 3 \\ log( {4}^{x} ) = log(3) \\ log( {2}^{2} )^{x} = log(3) \\ 2x log(2) = log(3) \\ 2x(0.3) = 0.48 \\ 0.6x = 0.48 \\ x = \frac{0.48}{0.6} = \frac{48}{6} = 8$

${2}^{x} = 0.5 \\ log( {2}^{x} ) = log(0.5) \\ x log(2) = log( \frac{1}{2} ) \\ x log(2) = log(1) - log(2) \\ x(0.3) = 0 - 0.3 \\ x = \frac{ - 0.3}{0.3} = - 1$

${8}^{x} = 45 \\ ( {2}^{3} )^{x} = 5 \times {3}^{2} \\ {2}^{3x} = 5 \times {3}^{2} \\ log( {2}^{3x} ) = log(5 \times {3}^{2} ) \\ 3x log(3) = log(5) + 2log(3) \\ 3x(0.48) = 0.7 + 2(0.48) \\ x = \frac{0.7 + 0.96}{3 \times 0.48} = \frac{83}{72}$

Espero que tenha te ajudado.

Bons estudos!