Solve -3 * e^-9x = -57

Question

A. X = -5.02
B. X = -4.25
C. X = -0.47
D. X = -0.33
Show your work simply

Answer 1

To solve the equation \(-3 e^{-9x} = -57\), we can follow these steps:

1. Divide both sides by -3: \[ e^{-9x} = \frac{-57}{-3} = 19 \]

2. Take the natural logarithm of both sides: \[ \ln(e^{-9x}) = \ln(19) \]

3. Simplify using the property of logarithms: \[ -9x = \ln(19) \]

4. Solve for \(x\) by dividing both sides by -9: \[ x = \frac{-\ln(19)}{9} \]

5. Calculate \(-\ln(19)\) using a calculator: \(\ln(19) \approx 2.944\) So, \[ -\ln(19) \approx -2.944 \]

6. Now, divide by 9: \[ x \approx \frac{-2.944}{9} \approx -0.3271 \]

After rounding, we can say:

\[ x \approx -0.33 \]

Therefore, the correct answer is D. X = -0.33.