Respuesta :

mhanifa

Answer:

A.

  • [tex]x^{x^3} = 3[/tex]
  • log [tex]x^{x^3}[/tex] = log 3
  • x³ log x = log 3
  • 3x³ log x = 3 log 3
  • x³ log x³ = log 3³
  • [tex]x^3^{x^3}[/tex] = 3³
  • x³ = 3
  • x = [tex]3^{1/3}[/tex]

B.

  • 4ˣ + 6ˣ = 9ˣ
  • 2²ˣ + 2ˣ3ˣ = 3²ˣ

Divide both sides by 2²ˣ

  • 1 + (3/2)ˣ = (3/2)²ˣ

Substitute (3/2)ˣ = t

  • t² - t - 1 = 0

Solve for t:

  • t = (1  ± √5)/2

Positive root is considered as (3/2)ˣ can't be negative.

  • (3/2)ˣ = (1 + √5)/2
  • x = log [(1 + √5)/2] / log (3/2)
  • x = 1.18681439028

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