sum of roots

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The sum of roots of the equation
x + 1 - 2 log₂ (2^x + 3) + 2 log₄ (10 - 2^-x) = 0 is

a) log₂11
b) log₂12
c) log₂13
d) log₂14

#Mathematics #Algebra

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Aditya Bhutra ·2012-03-28 04:17:50

i am getting a)

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rancho6 ·2012-03-28 04:54:50

how? please give detailed sol.

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mohit_ sharma ·2012-03-28 05:30:37

x+1 - 4log₄(2^x+3)+2log₄(10-2^-x)=0
this gives
2^-(x+1) = (10-2^-x)/(2^x+3)²
â†’ 2^2x -14.2^x + 11=0
put 2^x =t
this gives 2^x =7Â± âˆš38
x= log₂(7Â±âˆš38)
thus x₁ + x₂ =log₂11

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mohit_ sharma ·2012-03-28 05:41:27

so ans should be (a)

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fahadnasir nasir ·2012-03-30 12:57:36

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Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

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+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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sum of roots

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