To solve the equation \( 2 \cdot 3x = 8 \) for \( x \), follow these steps:

1. **Divide both sides by 2** to isolate the term involving \( x \):
   \[
   3x = \frac{8}{2}
   \]
   \[
   3x = 4
   \]

2. **Take the logarithm of both sides**. Since the equation is in the form \( 3x \), we can take the natural logarithm (ln) or logarithm with any base. Here, we use the natural logarithm:
   \[
   \ln(3x) = \ln(4)
   \]

3. **Use the logarithm power rule** (which states that \( \ln(a^b) = b\ln(a) \)) to bring the exponent down:
   \[
   x \cdot \ln(3) = \ln(4)
   \]

4. **Solve for \( x \)** by dividing both sides by \( \ln(3) \):
   \[
   x = \frac{\ln(4)}{\ln(3)}
   \]

So, the exact solution is:
\[
x = \frac{\ln(4)}{\ln(3)}
\]

Would you like any further explanation or have any questions?

Here are five related questions you might find interesting:

1. How would you solve \( 5^x = 7 \) for \( x \)?
2. What is the approximate value of \( \frac{\ln(4)}{\ln(3)} \)?
3. How would you solve \( 2x = 9 \) for \( x \)?
4. What is the general method to solve exponential equations like \( a^x = b \)?
5. How does the base of the logarithm affect the solution to the equation?

**Tip:** When dealing with exponential equations, taking the logarithm is a powerful tool to isolate the variable in the exponent.

Learn how to solve the equation 2 * 3x = 8 step-by-step with detailed explanations. This problem involves equations, logarithms, and exponents, applying the logarithm power rule to isolate the variable. Suitable for high school students.

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