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

The answer to e^{x-3}+e^{3-x}=2sqrt(2) is x=ln(1+sqrt(2))+3,x=ln(sqrt(2)-1)+3

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

e^{x - 3} + e^{3 - x} = 22

x = ln (1 + 2) + 3, x = ln (2 - 1) + 3

Decimal Notation

x = 3.88137 \dots, x = 2.11862 \dots

Solution steps

e^{x - 3} + e^{3 - x} = 22

Apply exponent rules

e^{x} e^{- 3} + (e^{x})^{- 1} e^{3} = 22

Rewrite the equation with

e^{x} = u

u e^{- 3} + (u)^{- 1} e^{3} = 22

Solve

u e^{- 3} + u^{- 1} e^{3} = 22 : u = e^{3} (1 + 2), u = e^{3} (2 - 1)

u = e^{3} (1 + 2), u = e^{3} (2 - 1)

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = e^{3} (1 + 2) : x = ln (1 + 2) + 3

Solve

e^{x} = e^{3} (2 - 1) : x = ln (2 - 1) + 3

x = ln (1 + 2) + 3, x = ln (2 - 1) + 3

16 + 2^{x} = 2^{x + 1}

e^{6 v + 5} - 1 = 67

2 7^{y} = 81

x e^{x} = 5

9^{3 x + 1} = 2 7^{2 x + 1}

What is the answer to e^{x-3}+e^{3-x}=2sqrt(2) ?
The answer to e^{x-3}+e^{3-x}=2sqrt(2) is x=ln(1+sqrt(2))+3,x=ln(sqrt(2)-1)+3