What is the answer to 4^x-9*2^x+8=0 ?

The answer to 4^x-9*2^x+8=0 is x=3,x=0

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4^x-9*2^x+8=0

4^{x} - 9 \cdot 2^{x} + 8 = 0

x = 3, x = 0

Solution steps

4^{x} - 9 \cdot 2^{x} + 8 = 0

Apply exponent rules

(2^{x})^{2} - 9 \cdot 2^{x} + 8 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} - 9 u + 8 = 0

Solve

u^{2} - 9 u + 8 = 0 : u = 8, u = 1

u = 8, u = 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = 1 : x = 0

x = 3, x = 0

e^{3 x} = 6 e^{x}

5^{x} = 12

x, e^{x} = 0

e^{2 x} - 7 e^{x} + 10 = 0

(3^{x} + 2)^{2} = 121