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Popular >

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

Solution

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

Solution

x = ln (3)

+1

Decimal Notation

x = 1.09861 \dots

Solution steps

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

Apply exponent rules

e^{x} - 3 (e^{x})^{- 1} = 2

Rewrite the equation with

e^{x} = u

u - 3 (u)^{- 1} = 2

Solve

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

u = 3, u = - 1

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 3 : x = ln (3)

Solve

e^{x} = - 1 :

No Solution for

x \in R

x = ln (3)

Popular Examples

5^x+5=2*5^{2-x}

5^{x} + 5 = 2 \cdot 5^{2 - x}

e^x-6e^{-x}+1=0

e^{x} - 6 e^{- x} + 1 = 0

3 \cdot 3^{x} = 27

7^{x} = 7

x^{ln(x)}=e^{100}

x^{l n (x)} = e^{100}

Frequently Asked Questions (FAQ)

What is the answer to e^x-3e^{-x}=2 ?
The answer to e^x-3e^{-x}=2 is x=ln(3)