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

$\mathrm{log}_{a}64=2$

Write down the value of $a$.

Find the value of $\mathrm{log}_{2}16$

$y=10^{x}$

Write $x$ in terms of $y$.

$x=$......................

Solve.

$\mathrm{log}2x=5$

$x=$..............

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:

$H=A\times b^{n}$

(i) Write down the value of $A$and $b$.

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

Give your answer in the form $n=\mathrm{log}_{b}a$.

Find the value of $x$.

$log_{3} ( 4 x + 1 ) = 4$

$\log ( 5 x + 2 ) = 2$

Find the value of $x$.

Find the value of $log_{4} ( \frac{1}{16} )$

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

$P=1000\times a^{n}$

(i) Write down the value of $a$.

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

Make $x$ the subject of this formula.

$y=10^{x}$

$\log ( \frac{1}{3 x - 2} ) = - 2$

Find the value of $x$.

Find the value of log _ 3 ( fourth sqrt of 1 / 9 ) )

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

$P=200\times2^{n}$

(i) Write down the initial population, $P_{0}$, of the rabbits.

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

Extract:

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

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

Extract:

The population, P, at the end of n years is given by the formula P = 200 × 2^n

Find the exact time the population becomes 200 000.

Give your answer in the form $n=\frac{\mathrm{log}b}{\mathrm{log}a}$.