Solving simultaneous exponential equations

Question

In[1]: Solve[{(1 + k)^n == 0.6, (1 + k)^(n + 1) == 0.3}, {n, k}]

Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>

Out[1]: {{n -> 0.736966, k -> -0.5}}

In[2]: Solve[{2*(1 + k)^n == 1.2, (1 + k)^(n + 1) == 0.3}, {n, k}]

Solve::inex: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >>

Out[2]: Solve[{2 (1 + k)^n == 1.2, (1 + k)^(1 + n) == 0.3}, {n, k}]

Where is the problem with Mathematica, not able to divide by 2 in first equation?

Answer 1

You can tell Solve to use Reduce, Reference to Solve

Solve[{2*(1 + k)^n == 1.2, (1 + k)^(n + 1) == 0.3}, {n, k}, 
Method -> Reduce]
(*{{n -> ConditionalExpression[-1.4427 (-0.510826 + (0. + 6.28319 I) C[
     1]), C[1] \[Element] Integers], 
      k -> ConditionalExpression[-0.5, C[1] \[Element] Integers]}}*)

Answer 2

Solve[Rationalize@{2*(1 + k)^n == 1.2, (1 + k)^(n + 1) == 0.3}, {n,  k}, Reals]
(*
 {{n -> (-Log[3] + Log[5])/Log[2], k -> -(1/2)}}
*)

or:

Solve[{2*(1 + k)^n == 1.2, (1 + k)^(n + 1) == 0.3}, {n, k}, Reals]
(*
 {{n -> 0.736966, k -> -0.5}}
*)