24) -3e^(4x + 1) - 2 = -98

Explanation:

Step1: Isolate the exponential term

Add 2 to both sides of the equation: [-3e^{4x + 1}-2+2=-98 + 2] [-3e^{4x+1}=-96]

Step2: Solve for the exponential term

Divide both sides by - 3: [\frac{-3e^{4x + 1}}{-3}=\frac{-96}{-3}] [e^{4x+1}=32]

Step3: Take the natural - logarithm of both sides

[\ln(e^{4x + 1})=\ln(32)] Using the property (\ln(e^{a})=a), we get (4x + 1=\ln(32))

Step4: Isolate x

Subtract 1 from both sides: (4x=\ln(32)-1) Divide both sides by 4: (x=\frac{\ln(32)-1}{4})

Answer:

(x=\frac{\ln(32)-1}{4})