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Popular >

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

Solution

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

Solution

x = ln (2), x = 0

+1

Decimal Notation

x = 0.69314 \dots, x = 0

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

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

Solve

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

u = 2, u = 1

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 2 : x = ln (2)

Solve

e^{x} = 1 : x = 0

x = ln (2), x = 0

Popular Examples

2^{-3n}*4^{2n-2}=16

2^{- 3 n} \cdot 4^{2 n - 2} = 16

5^{2 x - 7} = 3125

(5^x)(5^{x-1})=10

(5^{x}) (5^{x - 1}) = 10

7^{5 x - 12} = 343

e^{c} = 4

Frequently Asked Questions (FAQ)

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