To solve this problem step by step:

1. Express the solution in terms of logarithms:

The equation is: $3e^x = 79$ Divide through by 3: $e^x = \frac{79}{3}$ Take the natural logarithm (ln) of both sides: $x = \ln\left(\frac{79}{3}\right)$

2. Decimal approximation:

Using a calculator: $\frac{79}{3} \approx 26.3333$ $x = \ln(26.3333) \approx 3.27$

Final Answer:

• In terms of logarithms: $\ln\left(\frac{79}{3}\right)$
• Decimal approximation: $x \approx 3.27$

Would you like a breakdown of any specific step?

Here are some related questions:

1. Why do we use natural logarithms to solve for $x$?
2. How do logarithms work in simplifying exponential equations?
3. Can this solution be expressed using base-10 logarithms?
4. How do we ensure decimal approximations are accurate?
5. What are other practical uses of logarithmic equations?

Tip: Always recheck logarithmic and exponential calculations for accuracy when using a calculator.