What is the answer to 9^x-4sqrt(3)\times 3^{x-1}+1=0 ?

The answer to 9^x-4sqrt(3)\times 3^{x-1}+1=0 is x= 1/2 ,x=-1/2

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9^x-4sqrt(3)\times 3^{x-1}+1=0

9^{x} - 43 \cdot 3^{x - 1} + 1 = 0

x = \frac{1}{2}, x = - \frac{1}{2}

Decimal Notation

x = 0.5, x = - 0.5

Solution steps

9^{x} - 43 \cdot 3^{x - 1} + 1 = 0

Apply exponent rules

(3^{x})^{2} - 4 \cdot 3^{x} \cdot 3^{- 0.5} + 1 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} - 4 u \cdot 3^{- 0.5} + 1 = 0

Solve

u^{2} - 4 u \cdot 3^{- 0.5} + 1 = 0 : u = 3, u = \frac{1}{3}

u = 3, u = \frac{1}{3}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = \frac{1}{2}

Solve

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

x = \frac{1}{2}, x = - \frac{1}{2}

6 e^{6 x - 12} = 336

3^{x} = 5^{2 x - 3}

3^{x} = 5^{2 x - 7}

6^{- 5 x - 7} = 70

8 e^{8 x} - e^{- x} = 0

What is the answer to 9^x-4sqrt(3)\times 3^{x-1}+1=0 ?
The answer to 9^x-4sqrt(3)\times 3^{x-1}+1=0 is x= 1/2 ,x=-1/2
Solve for x: 9^x-4sqrt(3)\times 3^{x-1}+1=0
The solution is x= 1/2 ,x=-1/2