Explain how to solve 3x − 4 = 6 using the change of base formula . 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, we first need to isolate the variable \( x \).

### Step 1: Isolate the variable
Start by adding 4 to both sides of the equation:

\[
3x - 4 + 4 = 6 + 4
\]

\[
3x = 10
\]

Next, divide both sides by 3 to solve for \( x \):

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

\[
x \approx 3.333
\]

### Using the Change of Base Formula

However, since you asked for the use of the change of base formula, let's interpret this in the context of logarithms. The change of base formula is typically used for logarithmic equations, and here’s how it works:

\[
\log_b a = \frac{\log_c a}{\log_c b}
\]

But in this linear equation \( 3x - 4 = 6 \), logarithms are not required. The solution \( x \approx 3.333 \) was obtained directly from the linear equation. The change of base formula is not applicable to this type of problem, as it is used to convert between different logarithmic bases, not for solving linear equations.

Thus, the solution for \( x \) is:

\[
x \approx 3.333
\]

### Final Answer

\[
\boxed{3.333}
\]

### Summary

In summary, the equation \( 3x - 4 = 6 \) was solved by first isolating \( x \) to find that \( x \approx 3.333 \). The change of base formula is not applicable to solving this type of linear equation.

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Do you have any questions or would you like more details?

Here are 8 related questions:
1. What is the change of base formula and how is it used?
2. How do you solve logarithmic equations using the change of base formula?
3. What are the steps to solve a linear equation?
4. How can you check the solution to a linear equation?
5. What is the difference between linear equations and logarithmic equations?
6. Can you apply logarithms to linear equations directly?
7. How do you round numbers to the nearest thousandth?
8. How do you solve an equation with multiple steps?

**Tip:** When solving equations, always perform the same operation on both sides to keep the equation balanced.

Learn how to solve the linear equation 3x − 4 = 6 using the change of base formula with a step-by-step solution. This problem covers linear equations and logarithmic concepts. Suitable for students in Grades 9-12.

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