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

The answer to 9^x-3^{x+1}=-2 is x=(ln(2))/(ln(3)),x=0

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

The solution is x=(ln(2))/(ln(3)),x=0

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9^{x} - 3^{x + 1} = - 2

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

Decimal Notation

x = 0.63092 \dots, x = 0

Solution steps

9^{x} - 3^{x + 1} = - 2

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

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

u = 2, u = 1

Substitute back

u = 3^{x},

solve for

x

Solve

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

Solve

3^{x} = 1 : x = 0

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

3^{2 x} = 12

8^{3 x + 1} = 12 8^{x - 2}

7^{x - 4} = 7^{8}

2^{3 - 8 w} = 18

1 0^{3 x - 1} = 1

What is the answer to 9^x-3^{x+1}=-2 ?
The answer to 9^x-3^{x+1}=-2 is x=(ln(2))/(ln(3)),x=0
Solve for x: 9^x-3^{x+1}=-2
The solution is x=(ln(2))/(ln(3)),x=0