IBDP Past Year Exam Questions – Exponents and Logarithms

1.   [M12/P1/TZ1]

Solve the equation  $2 – {\log }_3(x+7)={\log }_{\frac{1}{3}}2x$ .   [5 marks]

2.   [M13/P1/TZ1]

The first terms of an arithmetic sequence are  $\frac{1}{{\log }_{2}x}, \frac{1}{{\log }_{8}x}, \frac{1}{{\log }_{32}x}, \frac{1}{{\log }_{128}x},.....$

Find x if the sum of the first 20 terms of the sequence is equal to 100.   [6 marks]

3.   [M14/P1/TZ1]

Consider $a={\log }_{2}3\times {\log }_{3}4\times {\log }_{4}5\times ...\times {\log }_{31}32$ . Given that  $a\in \mathrm{\mathbb{Z}}$ , find the value of  $a$ .   [5 marks]

4.   [M14/P1/TZ2]

Solve the equation  $8^{x–1}=6^{3x}$ . Express your answer in terms of ln2 and ln3 .   [5 marks]

5.   [N13/P1/TZ0]

Solve the following equations:

(a)    ${\log }_2\left(x–2\right)={\log }_4\left(x^2 – 6x +12\right)$ ;   [3 marks]

(b)    $x^{\ln x}=e^{{\left(\ln x\right)}^3}$ .  [5 marks]

6.   [M09/P1/TZ1]

Let  $g\left(x\right)={\log }_5\left|2{\log }_3 x\right|$ . Find the product of the zeros of  $g$ .   [5 marks]