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Pearson Edexcel IAL Mathematics P2.5 Exponentials & logarithms Question Bank

Practise exponential graphs, logarithm laws and log-based equation solving, from sketch features to exact and decimal answers.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • sketch exponential curves, showing intercepts and horizontal asymptotes
  • use log laws to turn logarithmic equations into algebraic equations
  • take logarithms to solve exponential models and interpret constants in context

Covered syllabus points

P2.5.1 - y = ax and its graphP2.5.2 - Laws of logarithmsP2.5.3 - Solving equations using logarithms

P2.5 - Exponentials and logarithms question 1

[Maximum number: 3]

Sketch the curve with equation

y=a−x+4y=a^{-x}+4

where a is a constant and a>1
On your sketch show
- the coordinates of the point of intersection of the curve with the y-axis
- the equation of the asymptote to the curve.

Table for Question P2.5 - Exponentials and logarithms question 1 — Edexcel A-Level Mathematics AS

The table above shows corresponding values of x and y for y=3−12x+4y=3^{-\frac{1}{2} x}+4
The values of y are given to four significant figures, as appropriate.
Using the trapezium rule with all the values of y in the table,

P2.5 - Exponentials and logarithms question 2

[Maximum number: 8]

Question (a)

(a)

Given that

3log⁡3(2x−1)=2+log⁡3(14x−25)3 \log _{3}(2 x-1)=2+\log _{3}(14 x-25)

show that

2x3−3x2−30x+56=02 x^{3}-3 x^{2}-30 x+56=0
[ 4 ]

Question (b)

(b)

Hence, using algebra and showing each step of your working, solve

3log⁡3(2x−1)=2+log⁡3(14x−25)3\log_3(2x-1)=2+\log_3(14x-25)

[ 4 ]

P2.5 - Exponentials and logarithms question 3

[Maximum number: 3]

In this question you must show all stages of your working.

Solutions relying on calculator technology are not acceptable.

Hence solve

2×4x−2x+3=17×2x−1−42 \times 4^{x}-2^{x+3}=17 \times 2^{x-1}-4
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