What is the answer to (e^x+e^{-x})/2 =3 ?

The answer to (e^x+e^{-x})/2 =3 is x=ln(3+2sqrt(2)),x=ln(3-2sqrt(2))

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(e^x+e^{-x})/2 =3

\frac{e ^{x} + e ^{- x}}{2} = 3

x = ln (3 + 22), x = ln (3 - 22)

Decimal Notation

x = 1.76274 \dots, x = - 1.76274 \dots

Solution steps

\frac{e ^{x} + e ^{- x}}{2} = 3

Multiply both sides by

2

\frac{e ^{x} + e ^{- x}}{2} \cdot 2 = 3 \cdot 2

Simplify

e^{x} + e^{- x} = 6

Apply exponent rules

e^{x} + (e^{x})^{- 1} = 6

Rewrite the equation with

e^{x} = u

u + (u)^{- 1} = 6

Solve

u + u^{- 1} = 6 : u = 3 + 22, u = 3 - 22

u = 3 + 22, u = 3 - 22

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 3 + 22 : x = ln (3 + 22)

Solve

e^{x} = 3 - 22 : x = ln (3 - 22)

x = ln (3 + 22), x = ln (3 - 22)

8^{x} = \frac{2 ^{56} - 4 ^{26}}{30}

98 e^{\frac{x}{2}} = 490

1 0^{x - 2} = 1000

3^{5 x + 1} = 27

5^{x} = 255

What is the answer to (e^x+e^{-x})/2 =3 ?
The answer to (e^x+e^{-x})/2 =3 is x=ln(3+2sqrt(2)),x=ln(3-2sqrt(2))