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Popular >

3e^x+6e^{-x}=11

Solution

3 e^{x} + 6 e^{- x} = 11

Solution

x = ln (3), x = ln (\frac{2}{3})

+1

Decimal Notation

x = 1.09861 \dots, x = - 0.40546 \dots

Solution steps

3 e^{x} + 6 e^{- x} = 11

Apply exponent rules

3 e^{x} + 6 (e^{x})^{- 1} = 11

Rewrite the equation with

e^{x} = u

3 u + 6 (u)^{- 1} = 11

Solve

3 u + 6 u^{- 1} = 11 : u = 3, u = \frac{2}{3}

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

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

e^{x} = \frac{2}{3} : x = ln (\frac{2}{3})

x = ln (3), x = ln (\frac{2}{3})

Popular Examples

3^2x+1-10(3^x)+3=0

3^{2} x + 1 - 10 (3^{x}) + 3 = 0

e^{5 x} = e^{15}

5^{2x}-5^x-20=0

5^{2 x} - 5^{x} - 20 = 0

5^x-2-5^x+5^x+1=5

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

6^{7 x} = 8

Frequently Asked Questions (FAQ)

What is the answer to 3e^x+6e^{-x}=11 ?
The answer to 3e^x+6e^{-x}=11 is x=ln(3),x=ln(2/3)