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Popular >

e^{2x}-9e^x+14=0

Solution

e^{2 x} - 9 e^{x} + 14 = 0

Solution

x = ln (7), x = ln (2)

+1

Decimal Notation

x = 1.94591 \dots, x = 0.69314 \dots

Solution steps

e^{2 x} - 9 e^{x} + 14 = 0

Apply exponent rules

(e^{x})^{2} - 9 e^{x} + 14 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} - 9 u + 14 = 0

Solve

u^{2} - 9 u + 14 = 0 : u = 7, u = 2

u = 7, u = 2

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 7 : x = ln (7)

Solve

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

x = ln (7), x = ln (2)

Popular Examples

8 1^{x} = \frac{1}{3}

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

5^{g^2-4g}=25^{-2}

5^{g^{2} - 4 g} = 2 5^{- 2}

4^{x-1}-18*2^{x-2}+8=0

4^{x - 1} - 18 \cdot 2^{x - 2} + 8 = 0

(2^{2-x})(4^{2x+3})=8

(2^{2 - x}) (4^{2 x + 3}) = 8

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-9e^x+14=0 ?
The answer to e^{2x}-9e^x+14=0 is x=ln(7),x=ln(2)