What is the answer to e^{2x}-10e^x+24=0 ?

The answer to e^{2x}-10e^x+24=0 is x=ln(6),x=2ln(2)

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e^{2x}-10e^x+24=0

e^{2 x} - 10 e^{x} + 24 = 0

x = ln (6), x = 2 ln (2)

Decimal Notation

x = 1.79175 \dots, x = 1.38629 \dots

Solution steps

e^{2 x} - 10 e^{x} + 24 = 0

Apply exponent rules

(e^{x})^{2} - 10 e^{x} + 24 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} - 10 u + 24 = 0

Solve

u^{2} - 10 u + 24 = 0 : u = 6, u = 4

u = 6, u = 4

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

e^{x} = 4 : x = 2 ln (2)

x = ln (6), x = 2 ln (2)

3 = 1 0^{x}

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

3^{x - 1} = 4

2^{x + 4} = e^{3 x}

What is the answer to e^{2x}-10e^x+24=0 ?
The answer to e^{2x}-10e^x+24=0 is x=ln(6),x=2ln(2)