transcendental equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg71357] transcendental equation*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Wed, 15 Nov 2006 06:45:29 -0500 (EST)

Why Solve cannot deal with the following transcendental equation? Solve[{2^x + 4^y == 9, x == y}, {x, y}] \!\(Solve::"incnst" \(\(:\)\(\ \)\) "Inconsistent or redundant transcendental equation. After reduction, the bad equation is \!\(Log[2\ \^x]\/Log[2] - Log[2\^y]\/Log[2]\) == 0"\) Solve::ifun: Inverse functions are being used by Solve, so some solutions may \ not be found; use Reduce for complete solution information. Solve::svars: Equations may not give solutions for all "solve" variables. {{x -> Log[2^y]/Log[2]}} Reduce on the contrary works fine Reduce[{2^x + 4^y == 9, x == y}, {x, y}] C[1] â?? Integers && (x == (2*I*Pi*C[1])/Log[2] + (I*Pi + Log[(1/2)*(1 + Sqrt[37])])/Log[2] || x == (2*I*Pi*C[1])/Log[2] + Log[(1/2)*(-1 + Sqrt[37])]/Log[2]) && y == x and so does the following setting Solve[2^x + 4^y == 9 /. y -> x, x] Solve::ifun : Inverse functions are being used by Solve, so some solutions \ may not be found; use Reduce for complete solution information. {{x -> Log[(1/2)*(-1 + Sqrt[37])]/Log[2]}, {x -> (I*Pi + Log[(1/2)*(1 + Sqrt[37])])/Log[2]}} Dimitris