What is the answer to 2e^y+15e^{-y}=11 ?

The answer to 2e^y+15e^{-y}=11 is y=ln(3),y=ln(5/2)

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2e^y+15e^{-y}=11

2 e^{y} + 15 e^{- y} = 11

y = ln (3), y = ln (\frac{5}{2})

Decimal Notation

y = 1.09861 \dots, y = 0.91629 \dots

Solution steps

2 e^{y} + 15 e^{- y} = 11

Apply exponent rules

2 e^{y} + 15 (e^{y})^{- 1} = 11

Rewrite the equation with

e^{y} = u

2 u + 15 (u)^{- 1} = 11

Solve

2 u + 15 u^{- 1} = 11 : u = 3, u = \frac{5}{2}

u = 3, u = \frac{5}{2}

Substitute back

u = e^{y},

solve for

y

Solve

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

Solve

e^{y} = \frac{5}{2} : y = ln (\frac{5}{2})

y = ln (3), y = ln (\frac{5}{2})

2.16 = (1 + 0.12)^{n - 1}

x^{a} = e^{x - 1}

y, \frac{x ^{- 2}}{x ^{y}} = \frac{1}{x ^{12}}

2^{2 x - 1} = 4^{x} - 2

9^{x} - 6 = - 3^{x}

What is the answer to 2e^y+15e^{-y}=11 ?
The answer to 2e^y+15e^{-y}=11 is y=ln(3),y=ln(5/2)