What is the answer to 3^{2x-3}-4*3^{x-2}+1=0 ?

The answer to 3^{2x-3}-4*3^{x-2}+1=0 is x=2,x=1

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3^{2x-3}-4*3^{x-2}+1=0

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

x = 2, x = 1

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

u^{2} \cdot 3^{- 3} - 4 u \cdot 3^{- 2} + 1 = 0 : u = 9, u = 3

u = 9, u = 3

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

3^{x} = 3 : x = 1

x = 2, x = 1

2 (3)^{2 x} = 5

7^{2 x} - 8 \cdot 7^{x} + 7 = 0

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

8^{n} - 8^{n - 1} = 14

4^{x} = 0

What is the answer to 3^{2x-3}-4*3^{x-2}+1=0 ?
The answer to 3^{2x-3}-4*3^{x-2}+1=0 is x=2,x=1
Solve for x: 3^{2x-3}-4*3^{x-2}+1=0
The solution is x=2,x=1