IB Maths AA HL 2.9 Exponential and logarithmic functions Question Bank

Practise IB Mathematics SL/HL 2.9 by applying exponential and logarithmic functions methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 3]

Consider the function f defined by $f(x)=\ln \left(x^{2}-16\right)$ for x>4.
The following diagram shows part of the graph of f which crosses the x-axis at point A , with coordinates (a, 0). The line L is the tangent to the graph of f at the point B .

Figure for Question SL 2.9—Exponential and logarithmic functions question 1 — IB Maths AA HL

Find the exact value of a.

$\quad \ln \left(x^{2}-16\right)=0$

\begin{aligned} & \mathrm{e}^{0}=x^{2}-16(=1) \\ & x^{2}=17 \text { OR } x= \pm \sqrt{17} \end{aligned}

$a=\sqrt{17}$

All question bank results loaded

SL 2.9—Exponential and logarithmic functions question 1