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

The answer to 2^{x+1}-32sqrt(2)=2^x is x= 11/2

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2^{x+1}-32sqrt(2)=2^x

2^{x + 1} - 322 = 2^{x}

x = \frac{11}{2}

Decimal Notation

x = 5.5

Solution steps

2^{x + 1} - 322 = 2^{x}

Subtract

2^{x}

from both sides

2^{x + 1} - 322 - 2^{x} = 2^{x} - 2^{x}

Simplify

2^{x + 1} - 322 - 2^{x} = 0

Factor

2^{x + 1} - 322 - 2^{x} : 2^{x} - 322

2^{x} - 322 = 0

Add

322

to both sides

2^{x} - 322 + 322 = 0 + 322

Simplify

2^{x} = 322

Apply exponent rules

x = \frac{11}{2}

1 6^{- x - 1} = \frac{1}{4}

3^{1 - x} = \frac{1}{27}

3^{x} = 30

2^{- 100 x} = 0. 5^{x - 4}

3 + 2 e^{- x} = 6

What is the answer to 2^{x+1}-32sqrt(2)=2^x ?
The answer to 2^{x+1}-32sqrt(2)=2^x is x= 11/2
Solve for x: 2^{x+1}-32sqrt(2)=2^x
The solution is x= 11/2