What is the answer to 2^{2x+1}-2^{x+4}=2^{x+2}-32 ?

The answer to 2^{2x+1}-2^{x+4}=2^{x+2}-32 is x=3,x=1

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2^{2x+1}-2^{x+4}=2^{x+2}-32

2^{2 x + 1} - 2^{x + 4} = 2^{x + 2} - 32

x = 3, x = 1

Solution steps

2^{2 x + 1} - 2^{x + 4} = 2^{x + 2} - 32

Apply exponent rules

(2^{x})^{2} \cdot 2^{1} - 2^{x} \cdot 2^{4} = 2^{x} \cdot 2^{2} - 32

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{1} - u \cdot 2^{4} = u \cdot 2^{2} - 32

Solve

u^{2} \cdot 2^{1} - u \cdot 2^{4} = u \cdot 2^{2} - 32 : u = 8, u = 2

u = 8, u = 2

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = 2 : x = 1

x = 3, x = 1

2^{x + 4} - 2^{x + 2} = 1

4^{x} + 1 0^{x} = 2 5^{x}

\frac{1}{2 ^{x}} + \frac{1}{2 ^{x}} + \frac{1}{2 ^{x}} = 3

(2^{x})^{6} = (2^{9})^{2}

4^{x - 1} \cdot (0.5)^{3 - 2 x} = (\frac{1}{8})^{x}

What is the answer to 2^{2x+1}-2^{x+4}=2^{x+2}-32 ?
The answer to 2^{2x+1}-2^{x+4}=2^{x+2}-32 is x=3,x=1
Solve for x: 2^{2x+1}-2^{x+4}=2^{x+2}-32
The solution is x=3,x=1