What is the answer to solvefor x,e^{2x}-11e^x+30=0 ?

The answer to solvefor x,e^{2x}-11e^x+30=0 is x=ln(6),x=ln(5)

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solvefor x,e^{2x}-11e^x+30=0

solve for

x, e^{2 x} - 11 e^{x} + 30 = 0

x = ln (6), x = ln (5)

Decimal Notation

x = 1.79175 \dots, x = 1.60943 \dots

Solution steps

e^{2 x} - 11 e^{x} + 30 = 0

Apply exponent rules

(e^{x})^{2} - 11 e^{x} + 30 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} - 11 u + 30 = 0

Solve

u^{2} - 11 u + 30 = 0 : u = 6, u = 5

u = 6, u = 5

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

e^{x} = 5 : x = ln (5)

x = ln (6), x = ln (5)

3^{2 x} - 3^{x} - 2 = 0

1 0^{x} = 40

1 0^{x} = 50

1 0^{x} = 64

6^{3 x - 4} = 5^{2 x}

What is the answer to solvefor x,e^{2x}-11e^x+30=0 ?
The answer to solvefor x,e^{2x}-11e^x+30=0 is x=ln(6),x=ln(5)