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

Question

Show your work simply

Answer 1

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

1. Divide both sides by -1 to eliminate the negative signs: \[ 3 e^{-9x} = 57 \]

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

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

4. Use the property of logarithms \(\ln(e^a) = a\): \[ -9x = \ln(19) \]

5. Divide both sides by -9 to isolate \(x\): \[ x = \frac{-\ln(19)}{9} \]

That's the solution for \(x\): \[ x = -\frac{\ln(19)}{9} \]