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Popular >

e^{2x}-10e^x+9=0

Solution

e^{2 x} - 10 e^{x} + 9 = 0

Solution

x = 2 ln (3), x = 0

+1

Decimal Notation

x = 2.19722 \dots, x = 0

Solution steps

e^{2 x} - 10 e^{x} + 9 = 0

Apply exponent rules

(e^{x})^{2} - 10 e^{x} + 9 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} - 10 u + 9 = 0

Solve

u^{2} - 10 u + 9 = 0 : u = 9, u = 1

u = 9, u = 1

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 9 : x = 2 ln (3)

Solve

e^{x} = 1 : x = 0

x = 2 ln (3), x = 0

Popular Examples

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

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

2 e^{x} = 110

2^{x} = 1024

4^{- x} = 2^{x + 1}

e^{3 b} = 2 + b

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-10e^x+9=0 ?
The answer to e^{2x}-10e^x+9=0 is x=2ln(3),x=0