What is the answer to 2(3^{2x})-5(3^x)+2=0 ?

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

Solve for x: 2(3^{2x})-5(3^x)+2=0

The solution is x=(ln(2))/(ln(3)),x=-(ln(2))/(ln(3))

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2 (3^{2 x}) - 5 (3^{x}) + 2 = 0

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

Decimal Notation

x = 0.63092 \dots, x = - 0.63092 \dots

Solution steps

2 (3^{2 x}) - 5 (3^{x}) + 2 = 0

Apply exponent rules

2 (3^{x})^{2} - 5 \cdot 3^{x} + 2 = 0

Rewrite the equation with

3^{x} = u

2 (u)^{2} - 5 u + 2 = 0

Solve

2 u^{2} - 5 u + 2 = 0 : u = 2, u = \frac{1}{2}

u = 2, u = \frac{1}{2}

Substitute back

u = 3^{x},

solve for

x

Solve

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

Solve

3^{x} = \frac{1}{2} : x = - \frac{ln ( 2 )}{ln ( 3 )}

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

5 (6^{x}) = 13

e^{2 x} + 1 = 0

6 e^{- 4 x} = 2

873 \cdot 2^{x} = 97

5 (3^{x} - 6) = 10

What is the answer to 2(3^{2x})-5(3^x)+2=0 ?
The answer to 2(3^{2x})-5(3^x)+2=0 is x=(ln(2))/(ln(3)),x=-(ln(2))/(ln(3))
Solve for x: 2(3^{2x})-5(3^x)+2=0
The solution is x=(ln(2))/(ln(3)),x=-(ln(2))/(ln(3))