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Popular >

e^x+6e^{-x}-5=0

Solution

e^{x} + 6 e^{- x} - 5 = 0

Solution

x = ln (3), x = ln (2)

+1

Decimal Notation

x = 1.09861 \dots, x = 0.69314 \dots

Solution steps

e^{x} + 6 e^{- x} - 5 = 0

Apply exponent rules

e^{x} + 6 (e^{x})^{- 1} - 5 = 0

Rewrite the equation with

e^{x} = u

u + 6 (u)^{- 1} - 5 = 0

Solve

u + 6 u^{- 1} - 5 = 0 : u = 3, u = 2

u = 3, u = 2

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

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

x = ln (3), x = ln (2)

Popular Examples

57 = 1 5^{x}

solvefor x,xy-e^x+e^y=0 solve for

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

solvefor x,5(25^x)=3.125^y solve for

x, 5 (2 5^{x}) = 3.12 5^{y}

5^{x+3}=7^{4-3x}

5^{x + 3} = 7^{4 - 3 x}

2 7^{x - 1} = 9

Frequently Asked Questions (FAQ)

What is the answer to e^x+6e^{-x}-5=0 ?
The answer to e^x+6e^{-x}-5=0 is x=ln(3),x=ln(2)