What is the answer to 2^{x+3}=2^{x-2}+62 ?

The answer to 2^{x+3}=2^{x-2}+62 is x=3

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2^{x+3}=2^{x-2}+62

2^{x + 3} = 2^{x - 2} + 62

x = 3

Solution steps

2^{x + 3} = 2^{x - 2} + 62

Subtract

2^{x - 2}

from both sides

2^{x + 3} - 2^{x - 2} = 2^{x - 2} + 62 - 2^{x - 2}

Simplify

2^{x + 3} - 2^{x - 2} = 62

Factor

2^{x + 3} - 2^{x - 2} : 31 \cdot 2^{x - 2}

31 \cdot 2^{x - 2} = 62

Divide both sides by

31

2^{x - 2} = 2

Apply exponent rules

x - 2 = 1

Solve

x - 2 = 1 : x = 3

x = 3

e^{- 3 x} = 1

y, e^{x y} = 2 y

4 e^{2 x} x^{2} + 8 e^{2 x} x + 2 e^{2 x} = 0

y, e^{x y} = 4 y

1000 (1.03)^{t} = 5000

What is the answer to 2^{x+3}=2^{x-2}+62 ?
The answer to 2^{x+3}=2^{x-2}+62 is x=3
Solve for x: 2^{x+3}=2^{x-2}+62
The solution is x=3