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Popular >

e^{2x}-13e^x+42=0

Solution

e^{2 x} - 13 e^{x} + 42 = 0

Solution

x = ln (7), x = ln (6)

+1

Decimal Notation

x = 1.94591 \dots, x = 1.79175 \dots

Solution steps

e^{2 x} - 13 e^{x} + 42 = 0

Apply exponent rules

(e^{x})^{2} - 13 e^{x} + 42 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} - 13 u + 42 = 0

Solve

u^{2} - 13 u + 42 = 0 : u = 7, u = 6

u = 7, u = 6

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

e^{x} = 6 : x = ln (6)

x = ln (7), x = ln (6)

Popular Examples

e^{6 x - 5} = 19

solvefor x,e^{2x+2y+z}=1 solve for

x, e^{2 x + 2 y + z} = 1

solvefor y,e^y=0 solve for

y, e^{y} = 0

solvefor y,e^y=9 solve for

y, e^{y} = 9

3 \cdot 2^{5 x} = 6

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-13e^x+42=0 ?
The answer to e^{2x}-13e^x+42=0 is x=ln(7),x=ln(6)