What is the answer to 2^{x+4}(2^{x-4}-1)=2^x-16 ?

The answer to 2^{x+4}(2^{x-4}-1)=2^x-16 is x=4,x=0

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2^{x+4}(2^{x-4}-1)=2^x-16

2^{x + 4} (2^{x - 4} - 1) = 2^{x} - 16

x = 4, x = 0

Solution steps

2^{x + 4} (2^{x - 4} - 1) = 2^{x} - 16

Subtract

2^{x}

from both sides

2^{x + 4} (2^{x - 4} - 1) - 2^{x} = 2^{x} - 16 - 2^{x}

Simplify

2^{x + 4} (2^{x - 4} - 1) - 2^{x} = - 16

Factor

2^{x + 4} (2^{x - 4} - 1) - 2^{x} : 2^{x} (2^{x} - 17)

2^{x} (2^{x} - 17) = - 16

Rewrite the equation with

2^{x} = u

u (u - 17) = - 16

Solve

u (u - 17) = - 16 : u = 16, u = 1

u = 16, u = 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 16 : x = 4

Solve

2^{x} = 1 : x = 0

x = 4, x = 0

3 \cdot 4^{x} + 4 \cdot 2^{x} + 8 = 0

3^{x} = x^{4}

x, 0 = 2 e^{- x} x + (- e^{- x}) x^{2}

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

y, x = 1 0^{y}

What is the answer to 2^{x+4}(2^{x-4}-1)=2^x-16 ?
The answer to 2^{x+4}(2^{x-4}-1)=2^x-16 is x=4,x=0
Solve for x: 2^{x+4}(2^{x-4}-1)=2^x-16
The solution is x=4,x=0