What is the answer to 6e^{2x}-11e^x=-4 ?

The answer to 6e^{2x}-11e^x=-4 is x=ln(4/3),x=-ln(2)

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6e^{2x}-11e^x=-4

6 e^{2 x} - 11 e^{x} = - 4

x = ln (\frac{4}{3}), x = - ln (2)

Decimal

x = 0.28768 \dots, x = - 0.69314 \dots

Solution steps

6 e^{2 x} - 11 e^{x} = - 4

Apply exponent rules

6 (e^{x})^{2} - 11 e^{x} = - 4

Rewrite the equation with

e^{x} = u

6 (u)^{2} - 11 u = - 4

Solve

6 u^{2} - 11 u = - 4 : u = \frac{4}{3}, u = \frac{1}{2}

u = \frac{4}{3}, u = \frac{1}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{4}{3} : x = ln (\frac{4}{3})

Solve

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

x = ln (\frac{4}{3}), x = - ln (2)

3^{x - 1} + 3^{x} + 3^{x + 1} = 351

12 8^{x} = 4 \times 2^{x}

3 x^{2} e^{- x} - x^{3} e^{- x} = 0

7^{x + 1} = 1

7^{x - 2} = 3^{2 - x}

What is the answer to 6e^{2x}-11e^x=-4 ?
The answer to 6e^{2x}-11e^x=-4 is x=ln(4/3),x=-ln(2)