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Sir I have an Equation $X^9 - X^3 = 24$. I solved it using Algebra, and the answer is $X = 1.44$ OR $\sqrt[3]{3}$. This is an Exponential Equation. Can this Equation be Solved using Logarithm ? If yes, then can you show me the steps, Hint, Clue ?

user2154420
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Nitin
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    What exactly do you mean by "exponential equation"? Because those are solutions, not exponential equations. – Deepak Feb 23 '23 at 02:28
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    $X^9-X^3=24$ is a polynomial of degree $9$, and specifically there is some polynomial $g$ of degree $3$ such that $X^9-X^3=24$ if and only if $g(X^3)=0$. Therefore the equation can be solved with Cardano's formula. The equation isn't "exponential" by any reasonable definition. – Sassatelli Giulio Feb 23 '23 at 02:39
  • To the best of my knowledge, when $~a,b \in \Bbb{R^+},~$ there is no simple way of expressing $~\ln(a - b)~$ in terms of $~\ln(a)~$ and $~\ln(b).$ – user2661923 Feb 23 '23 at 04:56

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