|
e
x
−
1
|
=
e
2
x
{
e
x
−
1
=
e
2
x
e
x
−
1
≥
0
∨
{
−
e
x
+
1
=
e
2
x
e
x
−
1
<
0
{
e
2
x
−
e
x
+
1
=
0
e
x
≥
1
∨
{
e
2
x
+
e
x
−
1
=
0
e
x
<
1
{
∄
x
∈
ℜ
e
x
≥
e
0
∨
{
e
x
=
−
1
+
5
2
∨
e
x
=
−
1
−
5
2
e
x
<
e
0
{
∄
x
∈
ℜ
∨
{
e
x
=
5
−
1
2
x
<
0
{
∄
x
∈
ℜ
∨
{
x
=
ln
5
−
1
2
x
<
0
{
∄
x
∈
ℜ
∨
{
x
=
ln
5
−
1
2
x
=
ln
5
−
1
2
abs{ e^x - 1 }=e^{ 2x } newline
left lbrace binom {e^x - 1 = e^2x} {e^x - 1 >= 0} right none or left lbrace binom {-e^x + 1 = e^2x} {e^x - 1 < 0} right none newline
left lbrace binom {e^2x-e^x+1=0} {e^x >=1} right none or left lbrace binom {e^2x+e^x - 1 =0} {e^x < 1} right none newline
left lbrace binom { notexists x in Re} {e^x >= e^0} right none or left lbrace binom {e^x={-1+sqrt 5}over {2} or e^x={-1-sqrt 5}over {2}} {e^x < e^0} right none newline
left lbrace { notexists x in Re } right none or left lbrace binom {e^x={sqrt 5 - 1}over {2} } {x<0} right none newline
left lbrace { notexists x in Re } right none or left lbrace binom {x=ln {sqrt 5 - 1}over {2} } {x<0} right none newline
left lbrace { notexists x in Re } right none or left lbrace {x=ln {sqrt 5 - 1}over {2} } right none newline
x=ln {sqrt 5 - 1}over {2}