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 (2^{x}) + 8 = 0

x = 2, x = 1

Solution steps

4^{x} - 6 (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

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

ln (2 + e^{- x}) = 2

e^{2 x} - 5 e^{x} = - 6

e^{2 x + 1} = 3

e^{- x} = \frac{1}{2}