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Study SL 2.9—Exponential and logarithmic functions conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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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 .

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 Topic Practice

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