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1.9 F: Exponentials and logarithms

1.9 F: Exponentials and logarithms

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Question 3

A curve has equation y=e2xy = e^{2x}y=e2x

a.

Find, in terms of aaa, the equation of the tangent to the curve at the point (a, e2a)\left(a,\, e^{2a}\right)(a,e2a).

[3]
b.

Find the value of a a\,a for which this tangent passes through the origin.

[2]
c.

Hence find the set of values of m m\,m for which the equation e2x=mxe^{2x} = mxe2x=mx has no real solutions.

[3]
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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