What is the answer to e^x+e^{-x}=7.4533 ?

The answer to e^x+e^{-x}=7.4533 is x=ln((7.4533+sqrt(51.55168…))/2),x=ln((7.4533-sqrt(51.55168…))/2)

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e^x+e^{-x}=7.4533

e^{x} + e^{- x} = 7.4533

x = ln (\frac{7.4533 + 51.55168 \dots}{2}), x = ln (\frac{7.4533 - 51.55168 \dots}{2})

Solution steps

e^{x} + e^{- x} = 7.4533

Apply exponent rules

e^{x} + (e^{x})^{- 1} = 7.4533

Rewrite the equation with

e^{x} = u

u + (u)^{- 1} = 7.4533

Solve

u + u^{- 1} = 7.4533 : u = \frac{7.4533 + 51.55168 \dots}{2}, u = \frac{7.4533 - 51.55168 \dots}{2}

u = \frac{7.4533 + 51.55168 \dots}{2}, u = \frac{7.4533 - 51.55168 \dots}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{7.4533 + 51.55168 \dots}{2} : x = ln (\frac{7.4533 + 51.55168 \dots}{2})

Solve

e^{x} = \frac{7.4533 - 51.55168 \dots}{2} : x = ln (\frac{7.4533 - 51.55168 \dots}{2})

x = ln (\frac{7.4533 + 51.55168 \dots}{2}), x = ln (\frac{7.4533 - 51.55168 \dots}{2})

x^{x} = 625

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2^{3^{x - 5}} = 8^{9^{x + 4}}

64 = 4^{a}

1 6^{x + 2} = 6 4^{2 x - 5}

What is the answer to e^x+e^{-x}=7.4533 ?
The answer to e^x+e^{-x}=7.4533 is x=ln((7.4533+sqrt(51.55168…))/2),x=ln((7.4533-sqrt(51.55168…))/2)