What is the answer to 2^x+4^x=3 ?

The answer to 2^x+4^x=3 is x=(ln((-1+sqrt(13))/2))/(ln(2))

Solve for x: 2^x+4^x=3

The solution is x=(ln((-1+sqrt(13))/2))/(ln(2))

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

x = \frac{ln ( \frac{- 1 + 13}{2} )}{ln ( 2 )}

Decimal Notation

x = 0.38158 \dots

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

u + (u)^{2} = 3

Solve

u + u^{2} = 3 : u = \frac{- 1 + 13}{2}, u = \frac{- 1 - 13}{2}

u = \frac{- 1 + 13}{2}, u = \frac{- 1 - 13}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = \frac{- 1 + 13}{2} : x = \frac{ln ( \frac{- 1 + 13}{2} )}{ln ( 2 )}

Solve

2^{x} = \frac{- 1 - 13}{2} :

No Solution for

x \in R

x = \frac{ln ( \frac{- 1 + 13}{2} )}{ln ( 2 )}

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729 \cdot (2^{n - 5})^{n} - 64 \cdot (3^{n})^{n - 5} = 0

4^{\frac{1}{( l o g _{2} ( x ) )}} = 2

8^{x} = 1 6^{- 1} \cdot 3 2^{x}

What is the answer to 2^x+4^x=3 ?
The answer to 2^x+4^x=3 is x=(ln((-1+sqrt(13))/2))/(ln(2))
Solve for x: 2^x+4^x=3
The solution is x=(ln((-1+sqrt(13))/2))/(ln(2))