4^x -10 • 4^-x = 3?
回答 (2)
2017-04-26 4:59 am
4ˣ - 10·4⁻ˣ = 3
multiply equation by 4ˣ
4ˣ·4ˣ - 10·4⁻ˣ·4ˣ = 3·4ˣ
4²ˣ - 10 = 3·4ˣ
4²ˣ - 3·4ˣ - 10 = 0
quadratic formula
4ˣ = [3 ± √(3² – 4·1(-10))] / [2·1]
= [3 ± √49] / 2
= [3 ± 7] /2
= -2, 5
-2 is an extraneous solution
4ˣ = 5
x = log₄(5) ≅ 1.1610
multiply equation by 4ˣ
4ˣ·4ˣ - 10·4⁻ˣ·4ˣ = 3·4ˣ
4²ˣ - 10 = 3·4ˣ
4²ˣ - 3·4ˣ - 10 = 0
quadratic formula
4ˣ = [3 ± √(3² – 4·1(-10))] / [2·1]
= [3 ± √49] / 2
= [3 ± 7] /2
= -2, 5
-2 is an extraneous solution
4ˣ = 5
x = log₄(5) ≅ 1.1610
2017-04-26 6:11 am
Presentation is unclear due to lack of brackets.
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