Question 1075852
.
using substitution y3^x solve the equation 3^x=2x+3^-x
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


In this case I will not use the substitution (since in this case it doesn't work at all).

I will use my common sense.


See the plot below, which shows the left side and the right side functions separately.


{{{graph( 330, 330, -1.5, 1.5, -1.5, 2.5,
          3^x, 2x + 3^(-x)
)}}}


Plots y = {{{3^x}}} (red) and y = {{{2x+3^(-x)}}} (green)


Looking into the plot, you can see immediately that x = 0 is the solution.
By finding the root visually, you can check it formally: it works.



Also, the plot gives you a clue that the equation has no other roots.