What is the answer to 16^x+16^{1-x}-10=0 ?

The answer to 16^x+16^{1-x}-10=0 is x= 3/4 ,x= 1/4

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16^x+16^{1-x}-10=0

1 6^{x} + 1 6^{1 - x} - 10 = 0

x = \frac{3}{4}, x = \frac{1}{4}

Decimal Notation

x = 0.75, x = 0.25

Solution steps

1 6^{x} + 1 6^{1 - x} - 10 = 0

Apply exponent rules

1 6^{x} + (1 6^{x})^{- 1} \cdot 1 6^{1} - 10 = 0

Rewrite the equation with

1 6^{x} = u

u + (u)^{- 1} \cdot 1 6^{1} - 10 = 0

Solve

u + u^{- 1} \cdot 1 6^{1} - 10 = 0 : u = 8, u = 2

u = 8, u = 2

Substitute back

u = 1 6^{x},

solve for

x

Solve

1 6^{x} = 8 : x = \frac{3}{4}

Solve

1 6^{x} = 2 : x = \frac{1}{4}

x = \frac{3}{4}, x = \frac{1}{4}

x^{x} = 2^{16}

5^{1 - x} = 6 - 5^{x}

5 (7)^{5 x} = 60

5^{n} = \frac{1}{125}

2^{x} = 3072

What is the answer to 16^x+16^{1-x}-10=0 ?
The answer to 16^x+16^{1-x}-10=0 is x= 3/4 ,x= 1/4
Solve for x: 16^x+16^{1-x}-10=0
The solution is x= 3/4 ,x= 1/4