What is the answer to a^2e^{ax}-3ae^{ax}+2=0 ?

The answer to a^2e^{ax}-3ae^{ax}+2=0 is x=(ln(-2/(a^2-3a)))/a

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a^2e^{ax}-3ae^{ax}+2=0

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

x = \frac{ln ( - \frac{2}{a ^{2} - 3 a} )}{a}

Solution steps

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

Move

2

to the right side

a^{2} e^{a x} - 3 a e^{a x} = - 2

Factor

a^{2} e^{a x} - 3 a e^{a x} : e^{a x} (a^{2} - 3 a)

e^{a x} (a^{2} - 3 a) = - 2

Divide both sides by

a^{2} - 3 a

e^{a x} = - \frac{2}{a ^{2} - 3 a}

Apply exponent rules

a x = ln (- \frac{2}{a ^{2} - 3 a})

Solve

a x = ln (- \frac{2}{a ^{2} - 3 a}) : x = \frac{ln ( - \frac{2}{a ^{2} - 3 a} )}{a}

x = \frac{ln ( - \frac{2}{a ^{2} - 3 a} )}{a}

4^{y + 1} = 6

2 = e^{0.08 t}

e^{x} = 1000000000

55 = 3 1^{x}

4^{x} + 4^{- x} = 7

What is the answer to a^2e^{ax}-3ae^{ax}+2=0 ?
The answer to a^2e^{ax}-3ae^{ax}+2=0 is x=(ln(-2/(a^2-3a)))/a