What is the answer to 4^x-5\times 2^x+4=0 ?

The answer to 4^x-5\times 2^x+4=0 is x=2,x=0

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4^x-5\times 2^x+4=0

4^{x} - 5 \cdot 2^{x} + 4 = 0

x = 2, x = 0

Solution steps

4^{x} - 5 \cdot 2^{x} + 4 = 0

Apply exponent rules

(2^{x})^{2} - 5 \cdot 2^{x} + 4 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} - 5 u + 4 = 0

Solve

u^{2} - 5 u + 4 = 0 : u = 4, u = 1

u = 4, u = 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 4 : x = 2

Solve

2^{x} = 1 : x = 0

x = 2, x = 0

2^{4 x + 1} = 3^{x}

4 e^{- x} x^{3} - e^{- x} x^{4} = 0

3^{x + 2} = 4^{x}

5^{x + 3} - 5^{x - 1} - 3120 = 0

1 0^{2 x - 3} = \frac{1}{10}

What is the answer to 4^x-5\times 2^x+4=0 ?
The answer to 4^x-5\times 2^x+4=0 is x=2,x=0
Solve for x: 4^x-5\times 2^x+4=0
The solution is x=2,x=0