Question

What is the value of x in the equation below?
1+2e^x+1=

Answer 1

It looks like the right-hand side is missing. I can handle the likely interpretations:

1) If you just want to simplify the expression
1 + 2e^x + 1 = 2 + 2e^x = 2(1 + e^x).

2) If the equation was 1 + 2e^x + 1 = 0, then
2 + 2e^x = 0 → 1 + e^x = 0 → e^x = −1,
which has no real solution. In complex form,
x = ln(−1) = iπ + 2π i k = (2k+1)iπ, k ∈ Z.

3) If the equation was 1 + 2e^x + 1 = A (some given A), then
2 + 2e^x = A → e^x = (A − 2)/2,
so a real solution exists only if (A − 2)/2 > 0, and then
x = ln((A − 2)/2).

Tell me the intended right-hand side if you want the specific x for that case.