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Popular >

e^x+15e^{-x}-8=0

Solution

e^{x} + 15 e^{- x} - 8 = 0

Solution

x = ln (5), x = ln (3)

+1

Decimal Notation

x = 1.60943 \dots, x = 1.09861 \dots

Solution steps

e^{x} + 15 e^{- x} - 8 = 0

Apply exponent rules

e^{x} + 15 (e^{x})^{- 1} - 8 = 0

Rewrite the equation with

e^{x} = u

u + 15 (u)^{- 1} - 8 = 0

Solve

u + 15 u^{- 1} - 8 = 0 : u = 5, u = 3

u = 5, u = 3

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 5 : x = ln (5)

Solve

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

x = ln (5), x = ln (3)

Popular Examples

3^{x-9}=81^{5x+1}

3^{x - 9} = 8 1^{5 x + 1}

3^{1 - 2 x} = 243

2^x+2^{x+1}= 3/2

2^{x} + 2^{x + 1} = \frac{3}{2}

3^{2x+1}-26(3^x)-9=0

3^{2 x + 1} - 26 (3^{x}) - 9 = 0

e^{x^2+1}=5e^{-x}

e^{x^{2} + 1} = 5 e^{- x}

Frequently Asked Questions (FAQ)

What is the answer to e^x+15e^{-x}-8=0 ?
The answer to e^x+15e^{-x}-8=0 is x=ln(5),x=ln(3)