Question 474229
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Presuming you mean:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ k\ -\ p(\ln(x))]


and not


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ (k\ -\ p)\ln(x)]


Add *[tex \Large -k] to both sides then multiply both sides by *[tex \Large -\frac{1}{p}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln(x)\ =\ \frac{k\ -\ A}{p}]


then use the definition of logarithms:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y = \log_b(x) \ \ \Rightarrow\ \ b^y = x]


to write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln(x)\ =\ \frac{k\ -\ A}{p} \ \ \Rightarrow\ x\ =\ e^{\left(\frac{k\ -\ A}{p}\right)}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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