# Exponential equation solver?

**URL:** <https://discourse.julialang.org/t/exponential-equation-solver/88807>\
**Category:** New to Julia\
**Created:** [October 16, 2022, 5:05pm UTC](https://discourse.julialang.org/t/exponential-equation-solver/88807 "2022-10-16T17:05:36Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![lesshaste](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lesshaste/32/12302_2.png) [@lesshaste](https://discourse.julialang.org/u/lesshaste)\
**Post date:** [October 16, 2022, 5:05pm UTC](https://discourse.julialang.org/t/exponential-equation-solver/88807/1 "2022-10-16T17:05:36Z")

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Is there a Julia package can solve exponential equations such as 4^x + 6^x == 9^x?

sympy can’t do this and I looked at Symbolics but I don’t think that can either.

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 16, 2022, 5:27pm UTC](https://discourse.julialang.org/t/exponential-equation-solver/88807/2 "2022-10-16T17:27:55Z")

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You can open an issue for Symbolics to one day do this, but I don’t think this is possible today. Today, doing it numerically with NonlinearSolve.jl is how I’d do it.

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**Author:** ![lesshaste](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lesshaste/32/12302_2.png) [@lesshaste](https://discourse.julialang.org/u/lesshaste)\
**Post date:** [October 16, 2022, 5:53pm UTC](https://discourse.julialang.org/t/exponential-equation-solver/88807/3 "2022-10-16T17:53:57Z")

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I have opened an issue. It really seems a shame if there is nothing to compete with sympy currently.

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**Author:** ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Post date:** [October 16, 2022, 10:59pm UTC](https://discourse.julialang.org/t/exponential-equation-solver/88807/4 "2022-10-16T22:59:30Z")

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> [@lesshaste](#):
>
> sympy can’t do this and I looked at Symbolics but I don’t think that can either.

Is there any symbolic-algebra software that can solve this kind of equation (symbolically)? It seems like the sort of thing that won’t generally have a closed-form solution?

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**Author:** ![jar1](https://avatars.discourse-cdn.com/v4/letter/j/c0e974/32.png) [@jar1](https://discourse.julialang.org/u/jar1)\
**Post date:** [October 16, 2022, 11:11pm UTC](https://discourse.julialang.org/t/exponential-equation-solver/88807/5 "2022-10-16T23:11:16Z")

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[exponential equations · Issue #764 · JuliaSymbolics/Symbolics.jl · GitHub](https://github.com/JuliaSymbolics/Symbolics.jl/issues/764) mentions

> **[4^x+6^x=9^x - Symbolab](https://www.symbolab.com/solver/step-by-step/4%5E%7Bx%7D%2B6%5E%7Bx%7D%3D9%5E%7Bx%7D?or=sug)**
>
> Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step

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<div class="post-metadata">

**Author:** ![lesshaste](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lesshaste/32/12302_2.png) [@lesshaste](https://discourse.julialang.org/u/lesshaste)\
**Post date:** [October 17, 2022, 10:23am UTC](https://discourse.julialang.org/t/exponential-equation-solver/88807/6 "2022-10-17T10:23:12Z")

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Wolfram Alpha and Symbolab can solve it quite happily. I don’t know if there are any open source libraries that can though.

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**Author:** ![Krastanov](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/krastanov/32/6817_2.png) [@Krastanov](https://discourse.julialang.org/u/Krastanov)\
**Post date:** [October 19, 2022, 2:54pm UTC](https://discourse.julialang.org/t/exponential-equation-solver/88807/7 "2022-10-19T14:54:48Z")

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I imagine most exponential equations do not conveniently convert into a single-variable polynomial equation, unlike the one you shared.

If you have some resources on standard techniques to use to efficiently detect whether your exponential equation can be converted like that, do mention it in the feature request issues on github. That would make it quite a bit more probable that someone would try to tackle them.