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

```

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