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Popular >

6e^{(-x)}-e^{(x)}=1

Solution

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

Solution

x = ln (2)

+1

Decimal Notation

x = 0.69314 \dots

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

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

Solve

6 u^{- 1} - u = 1 : u = - 3, u = 2

u = - 3, u = 2

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = - 3 :

No Solution for

x \in R

Solve

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

x = ln (2)

Popular Examples

3 \cdot 8^{x - 10} = 39

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

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

256^{n-3}=8^{2n}

25 6^{n - 3} = 8^{2 n}

2 = e^{0.02 \cdot t}

11(2^{3x+2})=352

11 (2^{3 x + 2}) = 352

Frequently Asked Questions (FAQ)

What is the answer to 6e^{(-x)}-e^{(x)}=1 ?
The answer to 6e^{(-x)}-e^{(x)}=1 is x=ln(2)