Question

Hi, how's everyone doing? I need help with these exponential equations, please. Thanks! :)​

Answer 1

Explanation:

1).
`2^{x^(2) +2x}=(1)/(2)`

`2^{x^(2) +2x}=2^(-1)`

Comparing exponents on both the sides.

x² + 2x = -1

x² + 2x + 1 = 0

(x + 1)² = 0

x = -1

2).
`2^(x-3)=8^(x+1)`

`2^(x-3)=(2^(3))^(x+1)`

`2^(x-3)=(2)^(3(x+1))`

By comparing exponents,

x - 3 = 3(x + 1)

x - 3 = 3x + 3

3x - x = 3 + 3

2x = 6

x = 3

3).
`\sqrt{a^(5-k)}=a^(3-k)`

`a^{(5-k)/(2)}=a^(3-k)`

By comparing exponents,

`(5-k)/(2)=3-k`

5 - k = 2(3 - k)

5 - k = 6 - 2k

2k - k = 6 - 5

k = 1

4).
`3^(x+3)=27^((2x+6))`

`3^(x+3)=(3^3)^(2x+6)`

`3^(x+3)=(3)^(3(2x+6))`

By comparing exponents,

x + 3 = 3(2x + 6)

x + 3 = 6x + 18

6x - x = 3 - 18

5x = - 15

x = -3

5).
`5^(x-2)=1`

`5^((x-2))=5^(0)`

x - 2 = 0

x = 2