What is the answer to 2e^{2x}-9e^x+4=0 ?

The answer to 2e^{2x}-9e^x+4=0 is x=2ln(2),x=-ln(2)

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2e^{2x}-9e^x+4=0

2 e^{2 x} - 9 e^{x} + 4 = 0

x = 2 ln (2), x = - ln (2)

Decimal Notation

x = 1.38629 \dots, x = - 0.69314 \dots

Solution steps

2 e^{2 x} - 9 e^{x} + 4 = 0

Apply exponent rules

2 (e^{x})^{2} - 9 e^{x} + 4 = 0

Rewrite the equation with

e^{x} = u

2 (u)^{2} - 9 u + 4 = 0

Solve

2 u^{2} - 9 u + 4 = 0 : u = 4, u = \frac{1}{2}

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

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 4 : x = 2 ln (2)

Solve

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

x = 2 ln (2), x = - ln (2)

512 = 1 \cdot 2^{n - 1}

x^{x^{49}} = 7^{7^{6}}

4^{x} = 0.5

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

3^{x} = 47

What is the answer to 2e^{2x}-9e^x+4=0 ?
The answer to 2e^{2x}-9e^x+4=0 is x=2ln(2),x=-ln(2)