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Popular >

e^x-5+4e^{-x}=0

Solution

e^{x} - 5 + 4 e^{- x} = 0

Solution

x = 2 ln (2), x = 0

+1

Decimal Notation

x = 1.38629 \dots, x = 0

Solution steps

e^{x} - 5 + 4 e^{- x} = 0

Apply exponent rules

e^{x} - 5 + 4 (e^{x})^{- 1} = 0

Rewrite the equation with

e^{x} = u

u - 5 + 4 (u)^{- 1} = 0

Solve

u - 5 + 4 u^{- 1} = 0 : u = 4, u = 1

u = 4, u = 1

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 4 : x = 2 ln (2)

Solve

e^{x} = 1 : x = 0

x = 2 ln (2), x = 0

Popular Examples

0=2e^x-9e^{-3x}

0 = 2 e^{x} - 9 e^{- 3 x}

1 0^{x^{2} - 1} = 1

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

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

9^{x} = 3^{x^{2} - 4 x}

2 \cdot 3^{x} = 5

Frequently Asked Questions (FAQ)

What is the answer to e^x-5+4e^{-x}=0 ?
The answer to e^x-5+4e^{-x}=0 is x=2ln(2),x=0