What is the answer to 4^x-6*2^x+8=0 ?

The answer to 4^x-6*2^x+8=0 is x=2,x=1

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4^x-6*2^x+8=0

4^{x} - 6 \cdot 2^{x} + 8 = 0

x = 2, x = 1

Solution steps

4^{x} - 6 \cdot 2^{x} + 8 = 0

Apply exponent rules

(2^{x})^{2} - 6 \cdot 2^{x} + 8 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} - 6 u + 8 = 0

Solve

u^{2} - 6 u + 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

15 \cdot 1 0^{x - 2} = 4^{x} \cdot 7

7^{- 9 x + 1} = 4 9^{- 12}

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

k, k (x) = x^{3} e^{2 x}

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