What is the answer to 2^{2x-1}-6\times 2^{x-1}+4=0 ?

The answer to 2^{2x-1}-6\times 2^{x-1}+4=0 is x=2,x=1

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2^{2x-1}-6\times 2^{x-1}+4=0

2^{2 x - 1} - 6 \cdot 2^{x - 1} + 4 = 0

x = 2, x = 1

Solution steps

2^{2 x - 1} - 6 \cdot 2^{x - 1} + 4 = 0

Apply exponent rules

(2^{x})^{2} \cdot 2^{- 1} - 6 \cdot 2^{x} \cdot 2^{- 1} + 4 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{- 1} - 6 u \cdot 2^{- 1} + 4 = 0

Solve

u^{2} \cdot 2^{- 1} - 6 u \cdot 2^{- 1} + 4 = 0 : u = 4, u = 2

u = 4, u = 2

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 4 : x = 2

Solve

2^{x} = 2 : x = 1

x = 2, x = 1

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

7 (3)^{x + 1} - 5^{x + 2} = 3^{x + 4} - 5^{x + 3}

16 = 0.5 \times 2^{x - 1}

3^{3 x + 5} = 3 \times 9^{x + 3}

2^{1 - 6 x} = 7^{3 x + 4}

What is the answer to 2^{2x-1}-6\times 2^{x-1}+4=0 ?
The answer to 2^{2x-1}-6\times 2^{x-1}+4=0 is x=2,x=1
Solve for x: 2^{2x-1}-6\times 2^{x-1}+4=0
The solution is x=2,x=1