What is the answer to 9^x-2\times 3^{x+2}+81=0 ?

The answer to 9^x-2\times 3^{x+2}+81=0 is x=2

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9^x-2\times 3^{x+2}+81=0

9^{x} - 2 \cdot 3^{x + 2} + 81 = 0

x = 2

Solution steps

9^{x} - 2 \cdot 3^{x + 2} + 81 = 0

Apply exponent rules

(3^{x})^{2} - 2 \cdot 3^{x} \cdot 3^{2} + 81 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} - 2 u \cdot 3^{2} + 81 = 0

Solve

u^{2} - 2 u \cdot 3^{2} + 81 = 0 : u = 9

u = 9

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

x = 2

8^{x} = 1024

e^{x} - e^{- 3} = 0

e^{2 x} - 12 = 4 e^{x}

2 - e^{- x} = 0

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

What is the answer to 9^x-2\times 3^{x+2}+81=0 ?
The answer to 9^x-2\times 3^{x+2}+81=0 is x=2
Solve for x: 9^x-2\times 3^{x+2}+81=0
The solution is x=2