What is the answer to 4^x-3*2^{x+1}+8=0 ?

The answer to 4^x-3*2^{x+1}+8=0 is x=2,x=1

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4^x-3*2^{x+1}+8=0

4^{x} - 3 \cdot 2^{x + 1} + 8 = 0

x = 2, x = 1

Solution steps

4^{x} - 3 \cdot 2^{x + 1} + 8 = 0

Apply exponent rules

(2^{x})^{2} - 3 \cdot 2^{x} \cdot 2^{1} + 8 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} - 3 u \cdot 2^{1} + 8 = 0

Solve

u^{2} - 3 u \cdot 2^{1} + 8 = 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

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

2^{5 x + 1} = 8 1^{x - 2}

5^{x^{2} - 5 x + 6} = 1

5^{x + 1} = 5^{2 x - 3}

2^{1 - x} = 3

What is the answer to 4^x-3*2^{x+1}+8=0 ?
The answer to 4^x-3*2^{x+1}+8=0 is x=2,x=1
Solve for x: 4^x-3*2^{x+1}+8=0
The solution is x=2,x=1