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Popular >

e^{2x}-5e^x+6=0

Solution

e^{2 x} - 5 e^{x} + 6 = 0

Solution

x = ln (3), x = ln (2)

+1

Decimal Notation

x = 1.09861 \dots, x = 0.69314 \dots

Solution steps

e^{2 x} - 5 e^{x} + 6 = 0

Apply exponent rules

(e^{x})^{2} - 5 e^{x} + 6 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} - 5 u + 6 = 0

Solve

u^{2} - 5 u + 6 = 0 : u = 3, u = 2

u = 3, u = 2

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

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

x = ln (3), x = ln (2)

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4 \times 3 - 2 \times 2

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\frac{2}{- 1}

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-5e^x+6=0 ?
The answer to e^{2x}-5e^x+6=0 is x=ln(3),x=ln(2)