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Popular >

2+e^{2x}=2+4e^{-x}

Solution

2 + e^{2 x} = 2 + 4 e^{- x}

Solution

x = \frac{2}{3} ln (2)

+1

Decimal Notation

x = 0.46209 \dots

Solution steps

2 + e^{2 x} = 2 + 4 e^{- x}

Apply exponent rules

2 + (e^{x})^{2} = 2 + 4 (e^{x})^{- 1}

Rewrite the equation with

e^{x} = u

2 + (u)^{2} = 2 + 4 (u)^{- 1}

Solve

Substitute back

u = e^{x},

solve for

x

Solve

x = \frac{2}{3} ln (2)

Popular Examples

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

5^{2x-1}=3^{x+7}

5^{2 x - 1} = 3^{x + 7}

e^{2 x} = 2.6

5^{x} = 1255

7776^{2x+4}=1296^{2x+1}

777 6^{2 x + 4} = 129 6^{2 x + 1}

Frequently Asked Questions (FAQ)

What is the answer to 2+e^{2x}=2+4e^{-x} ?
The answer to 2+e^{2x}=2+4e^{-x} is x= 2/3 ln(2)