What is the answer to 2^{x+2}+2^{x-3}=66 ?

The answer to 2^{x+2}+2^{x-3}=66 is x=4

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2^{x+2}+2^{x-3}=66

2^{x + 2} + 2^{x - 3} = 66

x = 4

Solution steps

2^{x + 2} + 2^{x - 3} = 66

Factor

2^{x + 2} + 2^{x - 3} : 33 \cdot 2^{x - 3}

33 \cdot 2^{x - 3} = 66

Divide both sides by

33

2^{x - 3} = 2

Apply exponent rules

x - 3 = 1

Solve

x - 3 = 1 : x = 4

x = 4

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

2 x e^{x} - 3 e^{x} = 0

4^{x} - 2^{x + 1} - 3 = 0

3 \cdot 4^{x} = 2 \cdot 1 2^{x}

2^{(- 3 x)} \cdot 4^{(2 x - 2)} = 16

What is the answer to 2^{x+2}+2^{x-3}=66 ?
The answer to 2^{x+2}+2^{x-3}=66 is x=4
Solve for x: 2^{x+2}+2^{x-3}=66
The solution is x=4