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Popular >

e^x-e^{-x}=5

Solution

e^{x} - e^{- x} = 5

Solution

x = ln (\frac{5 + 29}{2})

+1

Decimal Notation

x = 1.64723 \dots

Solution steps

e^{x} - e^{- x} = 5

Apply exponent rules

e^{x} - (e^{x})^{- 1} = 5

Rewrite the equation with

e^{x} = u

u - (u)^{- 1} = 5

Solve

u - u^{- 1} = 5 : u = \frac{5 + 29}{2}, u = \frac{5 - 29}{2}

u = \frac{5 + 29}{2}, u = \frac{5 - 29}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{5 + 29}{2} : x = ln (\frac{5 + 29}{2})

Solve

e^{x} = \frac{5 - 29}{2} :

No Solution for

x \in R

x = ln (\frac{5 + 29}{2})

Popular Examples

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log_{3}(27^{3x+4})=-2

lo g_{3} (2 7^{3 x + 4}) = - 2

9^{x} + 4 \cdot 3^{x} - 3 = 0

3^{2x}=6^{3x-1}

3^{2 x} = 6^{3 x - 1}

4^{5 x} = 7^{x + 3}

Frequently Asked Questions (FAQ)

What is the answer to e^x-e^{-x}=5 ?
The answer to e^x-e^{-x}=5 is x=ln((5+sqrt(29))/2)