Option (D)
Step-by-step explanation:
Given equation is,
![8e^{2x+1}=4](/tpl/images/1329/9610/6ce57.png)
Taking natural log on both the sides of the equation,
![\text{ln}(8e^{2x+1})=\text{ln}(4)](/tpl/images/1329/9610/52132.png)
![\text{ln}(2^3)+\text{ln}(e^{2x+1})=\text{ln}(2^2)](/tpl/images/1329/9610/a307e.png)
3ln(2) + (2x + 1)[ln(e)] = 2ln(2)
2n(2) - 3ln(2) = (2x + 1)
2x = -ln(2) - 1
[Since, -ln(2) = ln(1) - ln(2) =
]
![2x=\text{ln(0.5)}-1](/tpl/images/1329/9610/42594.png)
![x=\frac{\text{ln(0.5)-1}}{2}](/tpl/images/1329/9610/9b44f.png)
Therefore, Option (D) will be the correct option.