Solving a Tricky Exponential Equation | Math Olympiad Challenge

[@mohammedsaysrashid3587]

A wonderful introduction.👌.....x=-2 is a real solution

[@RashmiRay-c1y]

Let a = 2^(2x+4). Then, the given equation is written as a^3+2a^2=3. This has a=1 as the only real solution. So, 2x+4=0 > x = -2.

[@tunneloflight]

multiplicity 2 for each

[@roberttelarket4934]

(8^t, 4^t, 2^t) > 0.
If integers: 1 + 1 + 4 = 6.
x = -2 does the trick.
May be other roots.

[@StaR-uw3dc]

x=-2