Paper 1 June 2025, Question 3 1 mark
Express
as a single logarithm.
Circle your answer.
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AQA A Level Maths
Topic questions Pure mathematics Laws of logarithms
Laws of logarithms
8 questions · 42 marks · about 50 minutes
Laws of logarithms questions
TopicLaws of logarithms▾
AQA 7357 Laws of logarithms 8 questions
Paper 1 June 2025, Question 10 12 marks
Also involves Exponential growth and decay · Rearranging formulae
(a)
[3]
Show how
– kt θ = 21 – A e
can be rearranged to obtain
ln (21 – θ) = – kt + ln A
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(b)
The researcher uses measurements they have recorded to plot the graph of ln(21 – θ) against t as shown in the diagram below.
(b)(i)
[2]
Use the information on the graph to find the value of A
Give your answer to three significant figures.
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(b)(ii)
[2]
Use the information on the graph to find the value of k
Give your answer to three significant figures.
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(b)(iii)
[2]
Find the temperature of the dessert when it is initially removed from the freezer.
Give your answer to three significant figures.
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(c)
[3]
The dessert is ready to be eaten when its temperature reaches 4 °C
Use the model to determine the time, after being removed from the freezer, for the dessert to reach this temperature.
Give your answer to the nearest 10 minutes.
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Paper 3 June 2025, Question 4 3 marks
(a)
[1]
State the value of
where a > 0
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(b)
[2]
Find the value of
where a > 0
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Paper 1 June 2023, Question 6 5 marks
Show that the equation
2 log10 x 
log10 4 
log10 (x 
8)
has exactly one solution.
Fully justify your answer.
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Paper 2 June 2022, Question 9 4 marks
Also involves Indices · Surds
Given that
show that
where A is an integer and p is a rational number.
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Paper 1 June 2019, Question 1 1 mark
Given that a 
0, determine which of these expressions is not equivalent to the others.
Circle your answer.
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Paper 2 June 2019, Question 8 11 marks
Theresa bought a house on 2 January 1970 for £8000.
The house was valued by a local estate agent on the same date every 10 years up to 2010.
The valuations are shown in the following table.
| Year | 1970 | 1980 | 1990 | 2000 | 2010 |
| Valuation price | £8 000 | £19 000 | £36 000 | £82 000 | £205 000 |
The valuation price of the house can be modelled by the equation
where V pounds is the valuation price t years after 2 January 1970 and p and q are constants.
(a)
[2]
Show that V 
pqt can be written as log10 V 
log10 p 
t log10 q
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(b)
[4]
The values in the table of log 10 V against t have been plotted and a line of best fit has been drawn on the graph below.
Using the given line of best fit, find estimates for the values of p and q.
Give your answers correct to three significant figures.
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(c)
[3]
Determine the year in which Theresa’s house will first be worth half a million pounds.
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(d)
[2]
Explain whether your answer to part (c) is likely to be reliable.
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Paper 3 June 2018, Question 7 5 marks
Also involves Quadratic equations
(a)
[4]
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(b)
[1]
When asked to solve the equation
a student gives the following solution:
Explain what is wrong with the student’s solution.
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