How to solve exponential equations with unequal coefficients?

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  • Thread starter Thread starter Ali Asadullah
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SUMMARY

This discussion addresses the solution of exponential equations with unequal coefficients, specifically in the form eax + ebx = k. The method involves dividing through by ebx to transform the equation into a polynomial form y(a-b)/b - ky + 1 = 0, where y = e-bx. This polynomial equation is solvable if (a-b)/b is a positive integer; otherwise, it presents greater complexity. The discussion highlights the utility of Wolfram Alpha for solving such equations and providing step-by-step solutions.

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Ali Asadullah
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We know how to solve problems like e^ax+e^bx=k,
when a=2b. But how to solve equations of this type when a is not equal to 2b?
 
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Divide through by e^{bx} so that the equation becomes e^{(a-b)x}- ke^{-bx}+ 1= (e^{bx})^{(a-b)/b}- ke^{-bx}+ 1 0. Now let y= e^{-bx} and the equation is
y^{(a-b)/b}- ky+ 1= 0. That will be a polynomial equation if and only if (a-b)/b is a positive integer. Other wise it is a more difficult equation. There is no general method of solving such equations, not even all polynomial equations.
 
go to www.wolframalpha.com

it is very helpful with these kind of problems !

it sometimes also shows u step by step, how they got the answer, depending on question
 

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