# Another exponential equation issue

**URL:** <https://community.wolfram.com/t/another-exponential-equation-issue/1855>\
**Category:** Questions\
**Tags:** mathematica, equation-solving\
**Created:** [March 31, 2014, 10:28pm UTC](https://community.wolfram.com/t/another-exponential-equation-issue/1855 "2014-03-31T22:28:17Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![amyvgordon](https://avatars.discourse-cdn.com/v4/letter/a/eada6e/32.png) [@amyvgordon](https://community.wolfram.com/u/amyvgordon)\
**Post date:** [March 31, 2014, 10:28pm UTC](https://community.wolfram.com/t/another-exponential-equation-issue/1855/1 "2014-03-31T22:28:17Z")

</div>

I’m trying to solve two simultaneous exponential equations that should have one real solution for both a and b, but it produces loads of imaginary solutions, where am I going wrong?

```auto
Solve[{a Exp[b/2] == 25, a*Exp[10 b/3] == 16.9}, {a, b}]
Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>

```

---

<div class="post-metadata">

**Author:** ![dlkeith](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/dlkeith/32/31494_2.png) [@dlkeith](https://community.wolfram.com/u/dlkeith)\
**Post date:** [March 31, 2014, 11:04pm UTC](https://community.wolfram.com/t/another-exponential-equation-issue/1855/2 "2014-03-31T23:04:23Z")

</div>

Log(a) + b/2 == Log(25)  
Log(a) + 10 b/3 == Log(16.9)  
\>\>  
b/2 - Log(25) == 10 b/3 - Log(16.9)  
???

Computers make good servants but poor masters.  
-- Mr. Spock

```auto
In[205]:= Solve[{a Exp[b/2] == 25, a*Exp[10 b/3] == 16.9}, {a, 
  b}, Reals]

During evaluation of In[205]:= Solve::ratnz: Solve was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result. >>

Out[205]= {{a -> 26.7886, b -> -0.138198}}

```