What is the answer to 2^{x+2}+2^{x-2}+2^x=42 ?

The answer to 2^{x+2}+2^{x-2}+2^x=42 is x=3

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2^{x+2}+2^{x-2}+2^x=42

2^{x + 2} + 2^{x - 2} + 2^{x} = 42

x = 3

Solution steps

2^{x + 2} + 2^{x - 2} + 2^{x} = 42

Factor

2^{x + 2} + 2^{x - 2} + 2^{x} : 21 \cdot 2^{x - 2}

21 \cdot 2^{x - 2} = 42

Divide both sides by

21

2^{x - 2} = 2

Apply exponent rules

x - 2 = 1

Solve

x - 2 = 1 : x = 3

x = 3

9^{x} = 5

8 (8^{2 x}) + 23 (8^{x}) - 3 = 0

2^{2 x - 1} = \frac{1}{5 ^{2 x - 1}}

1 5^{- 9 x} = 5

4^{3 x - 4} = 1024

What is the answer to 2^{x+2}+2^{x-2}+2^x=42 ?
The answer to 2^{x+2}+2^{x-2}+2^x=42 is x=3
Solve for x: 2^{x+2}+2^{x-2}+2^x=42
The solution is x=3