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Popular >

e^x-7=2e^{-x}

Solution

e^{x} - 7 = 2 e^{- x}

Solution

x = ln (\frac{7 + 57}{2})

+1

Solution steps

e^{x} - 7 = 2 e^{- x}

Apply exponent rules

e^{x} - 7 = 2 (e^{x})^{- 1}

Rewrite the equation with

e^{x} = u

u - 7 = 2 (u)^{- 1}

Solve

u - 7 = 2 u^{- 1} : u = \frac{7 + 57}{2}, u = \frac{7 - 57}{2}

u = \frac{7 + 57}{2}, u = \frac{7 - 57}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{7 + 57}{2} : x = ln (\frac{7 + 57}{2})

Solve

e^{x} = \frac{7 - 57}{2} :

No Solution for

x \in R

x = ln (\frac{7 + 57}{2})

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9^{x} - 12 \cdot 3^{x} + 27 = 0

25^{2x}=sqrt(5)

2 5^{2 x} = 5

e^{- 4 x} = 3

5 e^{0.2 x} = 13

Frequently Asked Questions (FAQ)

What is the answer to e^x-7=2e^{-x} ?
The answer to e^x-7=2e^{-x} is x=ln((7+sqrt(57))/2)