What is the answer to e^{6x}-5e^{3x}+4=0 ?

The answer to e^{6x}-5e^{3x}+4=0 is x= 2/3 ln(2),x=0

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e^{6x}-5e^{3x}+4=0

e^{6 x} - 5 e^{3 x} + 4 = 0

x = \frac{2}{3} ln (2), x = 0

Decimal Notation

x = 0.46209 \dots, x = 0

Solution steps

e^{6 x} - 5 e^{3 x} + 4 = 0

Apply exponent rules

(e^{x})^{6} - 5 (e^{x})^{3} + 4 = 0

Rewrite the equation with

e^{x} = u

(u)^{6} - 5 (u)^{3} + 4 = 0

Solve

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 1 : x = 0

x = \frac{2}{3} ln (2), x = 0

e^{x} = e^{- x}

2 e^{- 2 x} = 5

e^{2 x} - 4 e^{x} + 3 = 0

8^{x} = 4

e^{x} = 6

What is the answer to e^{6x}-5e^{3x}+4=0 ?
The answer to e^{6x}-5e^{3x}+4=0 is x= 2/3 ln(2),x=0