Question

What is the solution to this equation?

Answer 1

Answer:

Option (D)

Step-by-step 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

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

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

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

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