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Exponentials & Logarithms (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

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Exponentials & Logarithms

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1
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log subscript a 64 space equals 2

Write down the value of a.

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2
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Find the value of log subscript 2 16

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3
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y equals 10 to the power of x

Write x in terms of y.

x equals......................

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4
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Solve.

log space 2 x equals 5

x equals..............

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51 mark

A small tree is initially 2 metres tall.
Each year, the height of the tree increases by 20%.

The height, H metres, of the tree at the end of n years is given by the formula:

H equals A cross times b to the power of n

(i) Write down the value of Aand b.

[2]

(ii) Find the exact time it takes for the tree to reach a height of 5 metres.

Give your answer in the form n equals log subscript b a.

[2]

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1
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log open parentheses 5 x plus 2 close parentheses equals 2

Find the value of x.

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2
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Find the value of log subscript 4 open parentheses 1 over 16 close parentheses

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3
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The population of a village is 1000 people.

Each year, the population decreases by 10%.

The population at the end of n years is given by the formula

P equals 1000 cross times a to the power of n

(i) Write down the value of a.

[1]

(ii) Find the exact time the population reaches 800.
Give your answer in an exact logarithm form.

[3]

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1
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log open parentheses fraction numerator 1 over denominator 3 x minus 2 end fraction close parentheses equals negative 2

Find the value of x.

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2
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Find the value of log subscript 3 open parentheses fourth root of 1 over 9 end root close parentheses

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3a
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A population of rabbits is increasing by the same amount each year.

The population, P, at the end of n years is given by the formula

P equals 200 cross times 2 to the power of n

(i) Write down the initial population, P subscript 0, of the rabbits.

[1]

(i) Write down the amount that the population increases by each year.

[1]

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3b
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After how many years will the population first exceed 10 000?

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3c
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Find the exact time the population becomes 200 000.

Give your answer in the form n equals fraction numerator log space b over denominator log space a end fraction.

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