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Another exponential equation issue

Posted 11 years ago
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?
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. >>
POSTED BY: Amy Gordon
Posted 11 years ago
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
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}}
POSTED BY: David Keith
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