What is the answer to 4^x+2^x=1 ?

The answer to 4^x+2^x=1 is x=(ln((-1+sqrt(5))/2))/(ln(2))

Solve for x: 4^x+2^x=1

The solution is x=(ln((-1+sqrt(5))/2))/(ln(2))

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

x = \frac{ln ( \frac{- 1 + 5}{2} )}{ln ( 2 )}

Decimal Notation

x = - 0.69424 \dots

Solution steps

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

Apply exponent rules

(2^{x})^{2} + 2^{x} = 1

Rewrite the equation with

2^{x} = u

(u)^{2} + u = 1

Solve

u^{2} + u = 1 : u = \frac{- 1 + 5}{2}, u = \frac{- 1 - 5}{2}

u = \frac{- 1 + 5}{2}, u = \frac{- 1 - 5}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = \frac{- 1 + 5}{2} : x = \frac{ln ( \frac{- 1 + 5}{2} )}{ln ( 2 )}

Solve

2^{x} = \frac{- 1 - 5}{2} :

No Solution for

x \in R

x = \frac{ln ( \frac{- 1 + 5}{2} )}{ln ( 2 )}

2^{x + 1} \times 1 6^{2 x + 1} = 3

102 4^{x + 1} = 1 6^{5}

x, f^{8 x + 11} = a^{9 x + 4}

e^{x} = 21

5^{x - 7} = \frac{1}{125}

What is the answer to 4^x+2^x=1 ?
The answer to 4^x+2^x=1 is x=(ln((-1+sqrt(5))/2))/(ln(2))
Solve for x: 4^x+2^x=1
The solution is x=(ln((-1+sqrt(5))/2))/(ln(2))