Which is the best approximation to a solution of the equation e^x = 2x + 3?

The correct question is 
Which is the best approximation to a solution of the equation
e^(2x) = 2e^{x) + 3?

we have that

e^(2x) = 2e^{x) + 3> e^(2x)- 2e^{x) - 3=0
the term 
e^(2x)- 2e^{x)> (e^x)²-2e^(x)*(1)+1²-1²> (e^x-1)²-1

then
e^(2x)- 2e^{x) - 3=0> (e^x-1)²-1-3=0> (e^x-1)²=4
(e^x-1)=2> e^x=3
x*ln(e)=ln(3)> x=ln(3)
ln(3)=1.10
hence
x=1.10

the answer is x=1.10