What is the answer to 9^x+2*3^{x+1}=1 ?

The answer to 9^x+2*3^{x+1}=1 is x=(ln(-3+sqrt(10)))/(ln(3))

Solve for x: 9^x+2*3^{x+1}=1

The solution is x=(ln(-3+sqrt(10)))/(ln(3))

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9^{x} + 2 \cdot 3^{x + 1} = 1

x = \frac{ln ( - 3 + 10 )}{ln ( 3 )}

Solution steps

9^{x} + 2 \cdot 3^{x + 1} = 1

Apply exponent rules

(3^{x})^{2} + 2 \cdot 3^{x} \cdot 3^{1} = 1

Rewrite the equation with

3^{x} = u

(u)^{2} + 2 u \cdot 3^{1} = 1

Solve

u^{2} + 2 u \cdot 3^{1} = 1 : u = - 3 + 10, u = - 3 - 10

u = - 3 + 10, u = - 3 - 10

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = - 3 + 10 : x = \frac{ln ( - 3 + 10 )}{ln ( 3 )}

Solve

3^{x} = - 3 - 10 :

No Solution for

x \in R

x = \frac{ln ( - 3 + 10 )}{ln ( 3 )}

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8^{2 - x} = 4^{3 x}

t, e^{k t} = 2

1 6^{- r - 1} = \frac{1}{4}

What is the answer to 9^x+2*3^{x+1}=1 ?
The answer to 9^x+2*3^{x+1}=1 is x=(ln(-3+sqrt(10)))/(ln(3))
Solve for x: 9^x+2*3^{x+1}=1
The solution is x=(ln(-3+sqrt(10)))/(ln(3))