IB Maths AA HL Sl 2 9 Exponential and Logarithmic Functions Questions

Practise IB Mathematics HL 2.9 by applying exponential and logarithmic functions methods to questions from the Question Bank.

Exam points

Analyse and graph exponential and logarithmic functions, including inverse relationships and asymptotes.
Solve exponential or logarithmic equations and interpret parameters using complete evidence.

[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 IB Maths AA HL Sl 2 9 Exponential and Logarithmic Functions Questions 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}

$a=\sqrt{17}$

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IB Maths AA HL Sl 2 9 Exponential and Logarithmic Functions Questions question 1