[?] Solve an equation and restrict solution to real numbers?

Questions
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1

When performing Solve[30000 == 25000 E^(k 10),k] I am getting a complex number as an answer. However when I enter Log[30000/25000]/10 I get the expected answer, which does not include a complex number and can not understand why - see attached?

Could someone please give me some clarification as to why the difference in results.

SolveQuestion.nb (3.66 KB)

2

Hi Mitchell,

Unless specified otherwise, Solve does not restrict the domain of the solution. There are infinitely many solutions in the complex domain for any integer value of C[1].

k -> ConditionalExpression[1/10 (2 I ? C[1] + Log[6/5]), C[1] ? Integers]

If you want to restrict the solution to Reals

Solve[30000 == 25000  E^(k  10), k, Reals]
(* {{k -> 0.0182322}} *)