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Popular >

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

Solution

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

Solution

x = ln (\frac{3 + 13}{2})

+1

Decimal Notation

x = 1.19476 \dots

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

u - (u)^{- 1} = 3

Solve

u - u^{- 1} = 3 : u = \frac{3 + 13}{2}, u = \frac{3 - 13}{2}

u = \frac{3 + 13}{2}, u = \frac{3 - 13}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{3 + 13}{2} : x = ln (\frac{3 + 13}{2})

Solve

e^{x} = \frac{3 - 13}{2} :

No Solution for

x \in R

x = ln (\frac{3 + 13}{2})

Popular Examples

2^{2t-1}=2^{t+5}

2^{2 t - 1} = 2^{t + 5}

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

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

2^{2 x} - 2^{x} - 2 = 0

8^{x + 4} = 2^{3}

3\times 2^{x+2}-5\times 2^{x-1}=76

3 \times 2^{x + 2} - 5 \times 2^{x - 1} = 76

Frequently Asked Questions (FAQ)

What is the answer to e^x-e^{-x}=3 ?
The answer to e^x-e^{-x}=3 is x=ln((3+sqrt(13))/2)