What is the answer to 2^x+4^x+8^x=266304 ?

The answer to 2^x+4^x+8^x=266304 is x=6

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2^x+4^x+8^x=266304

2^{x} + 4^{x} + 8^{x} = 266304

x = 6

Solution steps

2^{x} + 4^{x} + 8^{x} = 266304

Divide both sides by

2^{x}

\frac{2 ^{x}}{2 ^{x}} + \frac{4 ^{x}}{2 ^{x}} + \frac{8 ^{x}}{2 ^{x}} = \frac{266304}{2 ^{x}}

Simplify

1 + 2^{x} + 4^{x} = 4161 \cdot 2^{6 - x}

Apply exponent rules

1 + 2^{x} + (2^{x})^{2} = 4161 (2^{x})^{- 1} \cdot 2^{6}

Rewrite the equation with

2^{x} = u

1 + u + (u)^{2} = 4161 (u)^{- 1} \cdot 2^{6}

Solve

1 + u + u^{2} = 4161 u^{- 1} \cdot 2^{6} : u = 64

u = 64

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 64 : x = 6

x = 6

x, 1.0 8^{x} = 10

1 0^{\frac{x}{5}} = 57

e^{x} - 2 e^{- 2 x} = 0

40 0^{x} = \frac{1}{20}

1 0^{\frac{x}{2}} = 83

What is the answer to 2^x+4^x+8^x=266304 ?
The answer to 2^x+4^x+8^x=266304 is x=6
Solve for x: 2^x+4^x+8^x=266304
The solution is x=6