Question

1. Indicate all correct alternatives, where base of the log is 2. The equation x(3/4) (logx)* + logx=(5/4) = VE has : (A) at least one real solution (B) exactly three real solutions (C) exactly one irrational solution (D) complex roots​

Answer 1

Answer:

x^ 34(logx)^2 + logx - 5/4 = √(2) Let logx = a x = 2a (2^ 3a4)a^2 + a - 5/4 - √(2) = 0 Δ = 1 + 4(5/4 + √(2))(2^ 3a4) = 1 + (5 + 4√(2))2^(3a4)>0

Step-by-step explanation:

x^ 34(logx)^2 + logx - 5/4 = √(2) Let logx = a x = 2a (2^ 3a4)a^2 + a - 5/4 - √(2) = 0 Δ = 1 + 4(5/4 + √(2))(2^ 3a4) = 1 + (5 + 4√(2))2^(3a4)>0

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