find out the value of x, if x is a positive number such that 3x = 2log3

We have the equation \( 3x = 2 \log 3 \). To find the value of \( x \), we can solve the equation step by step.

1. Start with the given equation:
   \[
   3x = 2 \log 3
   \]

2. We need to isolate \( x \). Divide both sides of the equation by 3:
   \[
   x = \frac{2 \log 3}{3}
   \]

3. Simplify the expression:
   \[
   x = \frac{2 \log 3}{3}
   \]
   Since the problem asks for \( x \) as a positive number, we simply evaluate the right-hand side.

Therefore, the value of \( x \) is \( \frac{2 \log 3}{3} \).

If you need further details or have any questions, feel free to ask! Here are five related questions:

1. What is the numerical value of \( \log 3 \)?
2. How would the solution change if the base of the logarithm were different?
3. Can this equation have a negative solution for \( x \)?
4. How do you solve a logarithmic equation with variables in both the logarithm and the coefficient?
5. What is the significance of logarithmic functions in solving equations like this?

**Tip:** When solving equations with logarithms, make sure to understand the base of the logarithm and how it affects the solution.

Discover how to solve the equation 3x = 2 log 3 to find the value of x. This problem involves logarithmic equations and requires understanding logarithm properties. Suitable for advanced high school students.

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