What is the answer to 2^5+2^{x-1}=2^x ?

The answer to 2^5+2^{x-1}=2^x is x=6

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2^5+2^{x-1}=2^x

2^{5} + 2^{x - 1} = 2^{x}

x = 6

Solution steps

2^{5} + 2^{x - 1} = 2^{x}

Subtract

2^{x}

from both sides

2^{5} + 2^{x - 1} - 2^{x} = 2^{x} - 2^{x}

Simplify

32 + 2^{x - 1} - 2^{x} = 0

Factor

32 + 2^{x - 1} - 2^{x} : \frac{1}{2} (64 - 2^{x})

\frac{1}{2} (64 - 2^{x}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

64 - 2^{x} = 0

Solve

64 - 2^{x} = 0 : x = 6

x = 6

3^{2 - x} + 3^{3 - x} = 12

(- 5)^{x} = - 125

2^{x} = 400

0. 5^{x} = 1

5 (5^{2 x}) + 9 (5^{x}) - 2 = 0