Evaluate : A. x^(x^3)=3 B. 4^x +6^x =9^x

Question

Evaluate :
A.
`x^(x^3)=3`
B.
`4^x +6^x =9^x`

Answer 1

A.

• 
  `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)`

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