What is the answer to e^{2x}+9e^{-2x}-10=0 ?

The answer to e^{2x}+9e^{-2x}-10=0 is x=ln(3),x=0

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e^{2x}+9e^{-2x}-10=0

e^{2 x} + 9 e^{- 2 x} - 10 = 0

x = ln (3), x = 0

Solution steps

e^{2 x} + 9 e^{- 2 x} - 10 = 0

Apply exponent rules

(e^{x})^{2} + 9 (e^{x})^{- 2} - 10 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} + 9 (u)^{- 2} - 10 = 0

Solve

u^{2} + 9 u^{- 2} - 10 = 0 : u = 3, u = - 3, u = 1, u = - 1

u = 3, u = - 3, u = 1, u = - 1

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

e^{x} = - 3 :

No Solution for

x \in R

Solve

e^{x} = 1 : x = 0

Solve

e^{x} = - 1 :

No Solution for

x \in R

x = ln (3), x = 0

x, e^{x} - y^{2} = 0

\frac{18}{e ^{x} + 3} = 5

5^{x - 2} = \frac{1}{125}

2^{x} - 2 = 14

\frac{1}{2 ^{x - 3}} = 64

What is the answer to e^{2x}+9e^{-2x}-10=0 ?
The answer to e^{2x}+9e^{-2x}-10=0 is x=ln(3),x=0