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Exponentials and Logarithms

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Question 5

A curve has the equation y=ekxy = e^{kx}y=ekx, where k>0k>0k>0

a.

Find, in terms of a a\,a and kkk, the equation of the tangent to the curve at the point (a,eka)(a, e^{ka})(a,eka)

[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 ekx=mxe^{kx} = mxekx=mx has no real solutions.

[3]
Markscheme

Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /Exponentials and Logarithms

277 exam-style questions on Edexcel A Level Maths Exponentials and Logarithms, covering 14.1 Exponential Functions, 14.2 y = e^x, 14.3 Exponential Modelling, 14.4 Logarithms, 14.5 Laws of Logarithms, 14.6 Solving Equations using Logarithms, 14.7 Working with Natural Logarithms, and 14.8 Logarithms and Non-Linear Data. Each one has a worked solution and a mark scheme showing where the marks go.

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