4 power x +6 power x=9 power x
Answers
Answer: x=ln(1+root5/2)/ln(3/2)
Step-by-step explanation:
x = log( (1 + √5)/2 ) / log(3/2) or x = log ((-1 + √5)/2)/log(2/3)
Step-by-step explanation:
4ˣ + 6ˣ = 9ˣ
Dividing both sides by 4ˣ
=> 1 + (6/4)ˣ = (9/4)ˣ
=> 1 + (3/2)ˣ = ((3/2)²)ˣ
=> ((3/2)²)ˣ - (3/2)ˣ - 1 = 0
=> ((3/2)ˣ )² - (3/2)ˣ - 1 = 0
Let say (3/2)ˣ = y
=> y² - y - 1 = 0
=> y = (1 ± √5)/2
(3/2)ˣ = (1 ± √5)/2
Taking log both sides
x log(3/2) = log ((1 + √5)/2 ) as log of -ve not defined
=> x = log( (1 + √5)/2 ) / log(3/2)
x ≈ 1.1868
or
4ˣ + 6ˣ = 9ˣ
Dividing both sides by 9ˣ
=> (4/9)ˣ + (6/9)ˣ = 1
=> ((2/3)ˣ)² + (2/3)ˣ - 1 = 0
=> (2/3)ˣ = (-1 ± √5)/2
=> x = log ((-1 + √5)/2)/log(2/3)
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The two equations x^2 + y^2-12x-6y - 4 = 0 and x^2 + y^2
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4^x + 6^x = 9^x. Find the value of x
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