Question

What is the solution to this equation?

8(25 +1 = 4
СА.
In(0.5)
T =
- 1
OB.
Ос.
In(0.5) + 1
2
In(0.5)
+1
2
In(0.5) - 1
OD

Answer 1

Option (D)

Explanation:

Given equation is,

`8e^(2x+1)=4`

Taking natural log on both the sides of the equation,

`\text{ln}(8e^(2x+1))=\text{ln}(4)`

`\text{ln}(2^3)+\text{ln}(e^(2x+1))=\text{ln}(2^2)`

3ln(2) + (2x + 1)[ln(e)] = 2ln(2)

2n(2) - 3ln(2) = (2x + 1)

2x = -ln(2) - 1

`2x=\text{ln}((1)/(2))-1` [Since, -ln(2) = ln(1) - ln(2) =
`\text{ln}((1)/(2))`]

`2x=\text{ln(0.5)}-1`

`x=\frac{\text{ln(0.5)-1}}{2}`

Therefore, Option (D) will be the correct option.