Math Problem Statement

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

Solution

We have the equation 3x=2log33x = 2 \log 3. To find the value of xx, we can solve the equation step by step.

  1. Start with the given equation: 3x=2log33x = 2 \log 3

  2. We need to isolate xx. Divide both sides of the equation by 3: x=2log33x = \frac{2 \log 3}{3}

  3. Simplify the expression: x=2log33x = \frac{2 \log 3}{3} Since the problem asks for xx as a positive number, we simply evaluate the right-hand side.

Therefore, the value of xx is 2log33\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 log3\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 xx?
  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.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Equations

Formulas

Logarithm properties

Theorems

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Suitable Grade Level

Grades 11-12