I am trying to solve the secant problem here but i do not know how to derive the f(x). Question: Use secant method to approximate ln(2) to 3 decimal place, x_0= 0.6, X_1= 0.7 I need help.
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$\begingroup$ This Google search returns several pages explaining what the secant method is and how to use it, including a youtube video with an example (don't know if it's a good example or explanation since I haven't watched it). $\endgroup$– wltrupCommented Aug 2, 2015 at 22:47
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$\begingroup$ I have read through some but they have f(x) to be ax +3 and so forth nothing such as that above, so am confused. $\endgroup$– LynnieCommented Aug 2, 2015 at 22:52
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1$\begingroup$ Use $f(x)=e^x-2$. The example is not really persuasive, since we need to know how to evaluate the exponential function. $\endgroup$– André NicolasCommented Aug 2, 2015 at 23:17
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1 Answer
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The secant method is one method to find roots of functions, that is, given a function $f(x)$ and two pairs of values $(x_0, f(x_0))$ and $(x_1, f(x_1))$, it attempts to find the value of $x$ such that $f(x) = 0$.
You want to find the value of $\ln2$ so you need to express that problem in terms of the language of the secant method. The secant method gives you the value $x$ for which $f(x) = 0$. You want it to give you $\ln2$, though, so that means you want to find a function $f(x)$ such that $f(\ln2) = 0$.
You could choose $f(x) = e^x - 2$, for example. Note that $f(x) = 0$ implies $e^x = 2$ which is equivalent to $x = \ln2$. Then you need two starting values (and their corresponding $f$ values). You could choose $x_0 = 0$, for which you get $f(x_0) = -1$, and $x_1 = 1$, for which $f(x_1) = e - 2$.
The rest is just feeding numbers into the method and stopping when you get the desired number of significant digits.
