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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 3

Solution steps

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

Subtract

2^{x + 3}

from both sides

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

Simplify

2^{x - 2} + 62 - 2^{x + 3} = 0

Factor

2^{x - 2} + 62 - 2^{x + 3} : \frac{31}{4} (- 2^{x} + 8)

\frac{31}{4} (- 2^{x} + 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

- 2^{x} + 8 = 0

Solve

- 2^{x} + 8 = 0 : x = 3

x = 3

e^{2 x} = 10

2^{x - 1} = 31

e^{8 - 4 x} = 7

2 \cdot 4^{x} + 2^{3 - 2 x} = 17

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