How to solve exponential equations with unequal coefficients?

[Ali Asadullah]

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?

 

[HallsofIvy]

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.

 

[cloud360]

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