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

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

Find the value of $x$.

Find the value of ${\log }_4\left(\frac{1}{16}\right)$

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 $a$.

[1]

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

[3]

Make $x$ the subject of this formula.

$y={10}^x$

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

Find the value of $x$.

Find the value of ${\log }_3\left(\sqrt[4]{\frac{1}{9}}\right)$

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

$P=200\times 2^n$

(i) Write down the initial population, $P_0$, of the rabbits.

[1]

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

[1]

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

Find the exact time the population becomes 200 000.

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