Question

Please i need to know if im correct with these questions

Answer 1

Answer: No Solution

Explanation:

ln x - ln (x + 2) = 4 restrictions: x > 0 and x + 2 > 0 → x > 0

ln
`((x)/(x + 2))` = 4

`((x)/(x + 2))` = e⁴

x = e⁴ (x + 2)

x = 54.5982 (x + 2)

x = 54.5982x + 109.1964

- 53.5982x = 109.1964

x =
`(109.1964)/(-53.5982)`

x = -2.0373

-2.0373 is not greater than 0 so is not valid

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Answer: 2.1972

Explanation:

eˣ = 9

ln eˣ = ln 9

x = ln 9

x ≈ 2.1972

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Answer:
`(3)/(2)`

Explanation:

log₂ (3x - 4) = -1

3x - 4 = 2⁻¹

3x - 4 =
`(1)/(2)`

+4 +4

3x =
`4(1)/(2)`

3x =
`(9)/(2)`

`(3x)/(3) = (9)/(2) * (1)/(3)`

x =
`(3)/(2)`

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Answer: 1.117519

Explanation:

in the calculator, type in 1 ÷ 9.

Then hit the eˣ button.

e¹⁾⁹

= e°¹¹¹¹¹¹

= 1.117519

rounded to 6 decimal places: 1.117519