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Popular >

e^{2x}-14e^x+13=0

Solution

e^{2 x} - 14 e^{x} + 13 = 0

Solution

x = ln (13), x = 0

+1

Decimal

x = 2.56494 \dots, x = 0

Solution steps

e^{2 x} - 14 e^{x} + 13 = 0

Apply exponent rules

(e^{x})^{2} - 14 e^{x} + 13 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} - 14 u + 13 = 0

Solve

u^{2} - 14 u + 13 = 0 : u = 13, u = 1

u = 13, u = 1

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 13 : x = ln (13)

Solve

e^{x} = 1 : x = 0

x = ln (13), x = 0

Graph

Popular Examples

3^{2x-1}-8\times 3^{x-1}=3

3^{2 x - 1} - 8 \times 3^{x - 1} = 3

1 0^{4 x} = 72

6^{5 x} = 3000

e^{6x}-9e^{3x}-18=0

e^{6 x} - 9 e^{3 x} - 18 = 0

6^{-2x}*6^{-x}= 1/216

6^{- 2 x} \cdot 6^{- x} = \frac{1}{216}

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-14e^x+13=0 ?
The answer to e^{2x}-14e^x+13=0 is x=ln(13),x=0