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Popular >

(e^x+e^{-x})/2 =1

Solution

\frac{e ^{x} + e ^{- x}}{2} = 1

Solution

x = 0

Solution steps

\frac{e ^{x} + e ^{- x}}{2} = 1

Multiply both sides by

2

\frac{e ^{x} + e ^{- x}}{2} \cdot 2 = 1 \cdot 2

Simplify

e^{x} + e^{- x} = 2

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

u + (u)^{- 1} = 2

Solve

u + u^{- 1} = 2 : u = 1

u = 1

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 1 : x = 0

x = 0

Popular Examples

2^{2 x - 2} = 20

25^{2x+2}=(1/5)^{5x-1}

2 5^{2 x + 2} = (\frac{1}{5})^{5 x - 1}

4^{-2m-1}=4^{2m}

4^{- 2 m - 1} = 4^{2 m}

e^{x+1}=e^{2-x}

e^{x + 1} = e^{2 - x}

solvefor z,3^x=4^y=12^z solve for

z, 3^{x} = 4^{y} = 1 2^{z}

Frequently Asked Questions (FAQ)

What is the answer to (e^x+e^{-x})/2 =1 ?
The answer to (e^x+e^{-x})/2 =1 is x=0