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1.8 Exponentials and Logarithms

1.8 Exponentials and Logarithms

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Question 62

A telecommunications engineer is investigating the signal intensity, SSS (measured in picowatts), at a distance ddd (measured in metres) from a radio transmitter. The relationship is modelled by S=adbS = ad^bS=adb, where a a\,a and b b\,b are constants.

A graph shows a linear relationship between log⁡10S\log_{10} Slog10​S and log⁡10d\log_{10} dlog10​d. The line passes through the points (1,8)(1, 8)(1,8) and (4,2)(4, 2)(4,2).

a.

Find an equation linking log⁡10S\log_{10} Slog10​S with log⁡10d\log_{10} dlog10​d.

[3]
b.

Hence, or otherwise, express S S\,S in the form adbad^badb, where a a\,a and b b\,b are constants to be found.

[2]
Markscheme

1.8 Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /1.8 Exponentials and Logarithms

104 exam-style questions on OCR (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.

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