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Popular >

e^{2x}-8e^x+7=0

Solution

e^{2 x} - 8 e^{x} + 7 = 0

Solution

x = ln (7), x = 0

+1

Decimal Notation

x = 1.94591 \dots, x = 0

Solution steps

e^{2 x} - 8 e^{x} + 7 = 0

Apply exponent rules

(e^{x})^{2} - 8 e^{x} + 7 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} - 8 u + 7 = 0

Solve

u^{2} - 8 u + 7 = 0 : u = 7, u = 1

u = 7, u = 1

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

e^{x} = 1 : x = 0

x = ln (7), x = 0

Popular Examples

e^{2x}-9e^x+18=0

e^{2 x} - 9 e^{x} + 18 = 0

13 e^{5 x} = 13

5^{x} (3 - 5^{x}) = 2

x^{log_{10}(x)}=10000

x^{l o g_{10} (x)} = 10000

9^{x} - 7 (3^{x}) = 18

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-8e^x+7=0 ?
The answer to e^{2x}-8e^x+7=0 is x=ln(7),x=0