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1.9 F: Exponentials and logarithms

1.9 F: Exponentials and logarithms

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Question 5
a.

Using the substitution y=2xy = 2^xy=2x, show that the equation 4x−2x+2−5=04^x - 2^{x+2} - 5 = 04x−2x+2−5=0 can be written as y2−4y−5=0y^2 - 4y - 5 = 0y2−4y−5=0

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b.

Hence show that the equation 4x−2x+2−5=04^x - 2^{x+2} - 5 = 04x−2x+2−5=0 has x=log⁡25x = \log_2 5x=log2​5 as its only solution.

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Markscheme

1.9 F: Exponentials and logarithms Questions

  1. A Level
  2. /Maths
  3. /1.9 F: Exponentials and logarithms

62 exam-style questions on AQA A Level Maths 1.9 F: Exponentials and logarithms, covering 1.9.1 Exponential functions and their graphs, 1.9.2 Gradient of e^kx (A-level only), 1.9.3 Logarithms as inverse functions, 1.9.4 Laws of logarithms, 1.9.5 Solving exponential equations, 1.9.6 Logarithmic graphs to estimate parameters (A-level only), and 1.9.7 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.

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