are you sure the answer is -46.5 and that its not -93/2

Let's carefully review the steps to ensure the correct solution.

We start with the logarithmic equation:
\[
\log(7 - 2x) = 2
\]

1. **Convert the logarithmic equation to its exponential form**:
   \[
   7 - 2x = 10^2
   \]
   \[
   7 - 2x = 100
   \]

2. **Solve for \( x \)**:
   \[
   -2x = 100 - 7
   \]
   \[
   -2x = 93
   \]
   \[
   x = -\frac{93}{2}
   \]

So, the correct solution is indeed:
\[
x = -\frac{93}{2}
\]
This is equal to \(-46.5\) when expressed as a decimal.

Both \(-\frac{93}{2}\) and \(-46.5\) represent the same value. The answer in its exact form is \(-\frac{93}{2}\), while \(-46.5\) is the decimal form.

**Final Answer**:
A. \( x = -\frac{93}{2} \) or \( x = -46.5 \)

You can choose either form based on the context or instructions given.

---

Would you like further clarification or have any other questions?

Here are five related questions:
1. How do you determine whether to leave an answer in fractional form or convert it to a decimal?
2. What are some situations where a fractional answer is preferred over a decimal?
3. How do you check your answer when solving logarithmic equations?
4. How would you solve \( \log(3x - 5) = 1 \)?
5. How does the base of a logarithm affect the solution to an equation?

**Tip:** When solving equations, it’s often useful to keep the answer in fractional form for exactness, unless a decimal approximation is specifically required.

Explore the solution process for the logarithmic equation log(7 - 2x) = 2. Learn how to convert logarithmic equations to exponential form, solve for x, and interpret solutions in both fractional and decimal forms. Suitable for students in Grades 10-12.

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