Question-208263

Question Number 208263 by efronzo1 last updated on 09/Jun/24

Answered by Ghisom last updated on 09/Jun/24

a = e^{α} \Rightarrow b = e^{λ} a \land c = e^{2 λ} a

A = \log_{c} a = \frac{α}{α + 2 λ}

B = \log_{b} c = \frac{α + 2 λ}{α + λ}

C = \log_{a} b = \frac{α + λ}{α}

B - A = C - B = δ \Rightarrow

\frac{(3 α^{2} + 3 α λ - 2 λ^{2}) λ}{α (α + λ) (α + 2 λ)} = 0

λ = 0 \Rightarrow a = b = c \land δ = 1

λ = \frac{3 \pm \sqrt{33}}{4} α \Rightarrow δ = \frac{3}{2}

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