Question

select the correct answer.
what is the solution to this equation?
$8(e)^{2x + 1} = 4$
a. $x = \frac{\ln(0.5) + 1}{2}$
b. $x = \frac{\ln(0.5) - 1}{2}$
c. $x = \frac{\ln(0.5)}{2} - 1$
d. $x = \frac{\ln(0.5)}{2} + 1$

Explanation:

Step1: Isolate the exponential term

Divide both sides by 8:
$$e^{2x+1} = \frac{4}{8} = 0.5$$

Step2: Take natural log of both sides

Use $\ln(e^a)=a$ to simplify:
$$2x+1 = \ln(0.5)$$

Step3: Solve for $2x$

Subtract 1 from both sides:
$$2x = \ln(0.5) - 1$$

Step4: Solve for $x$

Divide both sides by 2:
$$x = \frac{\ln(0.5) - 1}{2}$$

Answer:

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