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'll go through a few steps. 

### Step 1: Isolate the term with the variable
First, add 4 to both sides of the equation to isolate the term with the variable \( x \):

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

This simplifies to:

\[
3x = 10
\]

### Step 2: Solve for \( x \)
Next, divide both sides of the equation by 3 to solve for \( x \):

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

\[
x \approx 3.333
\]

### Step 3: Check the Solution
To ensure the solution is correct, substitute \( x \approx 3.333 \) back into the original equation:

\[
3(3.333) - 4 \approx 9.999 - 4 = 5.999 \approx 6
\]

The left side is approximately equal to the right side, so the solution \( x \approx 3.333 \) is correct.

The change of base formula isn't typically needed for this kind of linear equation, as it's more relevant to logarithmic equations. Here, basic algebra suffices.

Would you like more details on any specific part of the process?

Here are 8 related questions:

1. How would you solve \( 5x + 2 = 17 \) using a similar method?
2. What if the equation was \( 4x - 3 = 9 \)? What would \( x \) be?
3. Can you explain how to solve \( 7x + 2 = 3x + 14 \)?
4. How do you use the change of base formula in logarithms?
5. What happens if the equation has no solution?
6. How would you solve \( 2x/3 = 4 \) for \( x \)?
7. What if the equation was \( 3(x - 2) = 9 \)? How would you solve for \( x \)?
8. Can you explain how to solve quadratic equations using the quadratic formula?

**Tip:** Always check your solution by substituting it back into the original equation.

Learn how to solve the equation 3x - 4 = 6 using the change of base formula with a step-by-step solution. This problem covers solving linear equations, isolating variables, and basic algebraic principles. Suitable for students in Grades 7-9.

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