Question

solve the equation $e^{5x} - 19 = 0$ using logarithmic form.

○ 0.512

○ 0.625

○ 0.325

○ 0.588

Explanation:

Step1: Isolate the exponential term

Start with the equation \( e^{5x} - 19 = 0 \). Add 19 to both sides to get \( e^{5x}=19 \).

Step2: Apply natural logarithm

Take the natural logarithm (ln) of both sides. Recall that \( \ln(e^{a}) = a \), so \( \ln(e^{5x})=\ln(19) \), which simplifies to \( 5x = \ln(19) \).

Step3: Solve for x

Divide both sides by 5: \( x=\frac{\ln(19)}{5} \). Calculate \( \ln(19)\approx2.9444 \), then \( x = \frac{2.9444}{5}\approx0.588 \).

Answer:

0.588