Q. Solve for x the equation 2ˣ⁺³ = 5ˣ⁺².

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Q. Given: log₄ z = B log₂/₃z, for all z > 0. Find the value of constant B.

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Q. Evaluate: 16ˣ – 4ˣ – 9 = 0.

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Q. Transform 54ʸ = n+1 into equivalent a logarithmic expression.

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Q. If logₐ\((\frac{1}{8}) = -\frac{3}{4}\), than what is x?

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Q. The explicit formula for the geometric sequence 3, 15, 75, 375,… is _______

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Q. The third term of a geometric progression with common ratio equal to half the initial term is 81. Determine the 12th term.

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Q. Which of the following series is called the “formal power series”?

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Q. Determine the interval and radius of convergence for the power series: ∞∑ₙ₌₁7ⁿ/n(3x−1)ⁿ⁻¹.

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Q. What is the radius of convergence and interval of convergence for the power series ∞∑ₙ₌₀m!(2x-1)ᵐ?

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Q. Determine the radius of convergence and interval of convergence for the power series: ∞∑ₙ₌₀ (x−7)ⁿ⁺¹/nⁿ.

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