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Popular >

e^x+2e^{-x}=4.5

Solution

e^{x} + 2 e^{- x} = 4.5

Solution

x = 2 ln (2), x = - ln (2)

+1

Decimal Notation

x = 1.38629 \dots, x = - 0.69314 \dots

Solution steps

e^{x} + 2 e^{- x} = 4.5

Apply exponent rules

e^{x} + 2 (e^{x})^{- 1} = 4.5

Rewrite the equation with

e^{x} = u

u + 2 (u)^{- 1} = 4.5

Solve

u + 2 u^{- 1} = 4.5 : u = 4, u = \frac{1}{2}

u = 4, u = \frac{1}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 4 : x = 2 ln (2)

Solve

e^{x} = \frac{1}{2} : x = - ln (2)

x = 2 ln (2), x = - ln (2)

Popular Examples

5^{x + 5} = 625

27 = 3^{x - 1}

7.7=860(0.5)^{x/6}

7.7 = 860 (0.5)^{\frac{x}{6}}

solvefor n,2r^n=1 solve for

n, 2 r^{n} = 1

7^{3 x + 2} = 42

Frequently Asked Questions (FAQ)

What is the answer to e^x+2e^{-x}=4.5 ?
The answer to e^x+2e^{-x}=4.5 is x=2ln(2),x=-ln(2)