What is the answer to 2^x+2^{6-x}=16 ?

The answer to 2^x+2^{6-x}=16 is x=3

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2^x+2^{6-x}=16

2^{x} + 2^{6 - x} = 16

x = 3

Solution steps

2^{x} + 2^{6 - x} = 16

Apply exponent rules

2^{x} + (2^{x})^{- 1} \cdot 2^{6} = 16

Rewrite the equation with

2^{x} = u

u + (u)^{- 1} \cdot 2^{6} = 16

Solve

u + u^{- 1} \cdot 2^{6} = 16 : u = 8

u = 8

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

x = 3

500 = 100 (2^{\frac{t}{5}})

4^{3 x + 1} = 64

2^{- x} (2^{- x} + 2) = 15

t, e^{k t} = \frac{1}{6}

t, e^{k t} = \frac{1}{5}