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SpyIntel [72]
3 years ago
11

Evaluate : A.

n="absmiddle" class="latex-formula">
B. 4^x +6^x =9^x
Mathematics
1 answer:
sdas [7]3 years ago
7 0

Answer:

<h3>A. </h3>
  • x^{x^3} = 3
  • log x^{x^3} = log 3
  • x³ log x = log 3
  • 3x³ log x = 3 log 3
  • x³ log x³ = log 3³
  • x^3^{x^3} = 3³
  • x³ = 3
  • x = 3^{1/3}
<h3>B.</h3>
  • 4ˣ + 6ˣ = 9ˣ
  • 2²ˣ + 2ˣ3ˣ = 3²ˣ

<u>Divide both sides by 2²ˣ</u>

  • 1 + (3/2)ˣ = (3/2)²ˣ

<u>Substitute (3/2)ˣ = t</u>

  • t² - t - 1 = 0

<u>Solve for t:</u>

  • t = (1  ± √5)/2

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

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

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