NSW Y12 Maths - Advanced Exponential and Log Function Log Functions

Resources for Log Functions

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Log Functions Theory

This subtopic is a revision of the subtopic in the year 11 course. \\  The solutions of exponential and logarithmic equations will be covered.\\  \begin{multicols}{2}  \textbf{Example 1}\\ %10643 Solve \({e^{2x}} - 2{e^x} - 8 = 0\)\\  \textbf{Example 1 solution}\\ $\begin{aligned}\text { Let } y=e^{x} \rightarrow y^{2}=e^{2 x} \\ y^{2}-2 y-8&=0 \\ (y-4)(y+2)&=0  \\ y=4,4&=-2  \\ e^{x}&=4\quad  e^{x} \neq-2 \\ \therefore\ x=& \log _{e} 4 \\ & =1.39 \end{aligned}$\\  \columnbreak \textbf{Example 2}\\ %7 (30976) Solve \(\ln(6 - x) = 2\ln x\)\\  \textbf{Example 2 solution}\\  $\begin{aligned} \ln(6 - x) &= \ln x^2\\ 6-x &= x^2 \qquad (\ln x \text{ is invertable})\\ x^2 + x - 6 &= 0\\(x + 3)(x - 2) &= 0\\ \therefore x = -3 &\text{ or } x = 2 \end{aligned}$\\  \(x = 2\) is the only valid solution since \(2\ln(-3)\) is not defined.   \end{multicols}

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Videos

Videos relating to Log Functions.

  • Log Functions - Video - Logs - How to solve equations where x is in the power

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