Explain how to solve 3x − 4 = 6 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

To solve the equation \(3x - 4 = 6\) using the change of base formula for logarithms, follow these steps:

1. **Isolate the term with \(x\):**

   \[
   3x - 4 = 6
   \]

   Add 4 to both sides:

   \[
   3x = 10
   \]

2. **Solve for \(x\):**

   \[
   x = \frac{10}{3}
   \]

   At this point, you can simplify:

   \[
   x \approx 3.333
   \]

Since the problem also mentions the change of base formula, let's apply it to understand its usage, even though it's not directly needed to solve this linear equation. The change of base formula for logarithms is:

\[
\log_b(y) = \frac{\log(y)}{\log(b)}
\]

However, since we are not dealing with logarithms in the equation \(3x - 4 = 6\), and we have already solved for \(x\) directly, there's no need to apply the change of base formula here.

The solution for \(x\), rounded to the nearest thousandth, is:

\[
x \approx 3.333
\]

Would you like more details or have any questions?

Here are 5 questions you might find interesting to ask next:
1. How do you solve quadratic equations using the quadratic formula?
2. Can you explain the process of completing the square?
3. How do you solve systems of linear equations using the substitution method?
4. What is the difference between permutations and combinations?
5. How do you find the derivative of a function using the definition of a derivative?

**Tip:** When solving equations, always check your solution by substituting it back into the original equation to verify its correctness.

Learn how to solve the equation 3x - 4 = 6 using the change of base formula for logarithms. Includes a detailed step-by-step solution and explanation. Suitable for students in Grades 9-12.

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