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Popular >

8e^{-x}-e^x=2

Solution

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

Solution

x = ln (2)

+1

Decimal Notation

x = 0.69314 \dots

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

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

Solve

8 u^{- 1} - u = 2 : u = - 4, u = 2

u = - 4, u = 2

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = - 4 :

No Solution for

x \in R

Solve

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

x = ln (2)

Popular Examples

3^{x+1}+3^x+3^{x-1}=39

3^{x + 1} + 3^{x} + 3^{x - 1} = 39

e^{- 9 x} = - 3

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

2^{x^{2} - 3 x} = 16

5^{x-2}-5^x+5^{x+1}=505

5^{x - 2} - 5^{x} + 5^{x + 1} = 505

Frequently Asked Questions (FAQ)

What is the answer to 8e^{-x}-e^x=2 ?
The answer to 8e^{-x}-e^x=2 is x=ln(2)