give me one logarithm question that needs to get solved by turning them into exponentials then solved for x

Sure! Here's a logarithm question that requires converting it into an exponential equation before solving for \( x \):

**Question:**  
Solve for \( x \):  
\[
\log_5 (x + 2) = 3
\]

### **Solution Steps:**
1. **Convert the logarithmic equation to an exponential form:**
   \[
   x + 2 = 5^3
   \]

2. **Simplify the exponent:**
   \[
   x + 2 = 125
   \]

3. **Solve for \( x \):**
   \[
   x = 125 - 2
   \]
   \[
   x = 123
   \]

So, the final answer is **\( x = 123 \)**.

Would you like a deeper explanation of logarithm-to-exponential conversion?  

### **Related Questions:**  
1. Solve \( \log_3 (x - 1) = 4 \) by converting to an exponential equation.  
2. Solve \( \log_7 (2x + 5) = 2 \).  
3. Find \( x \) in \( \log_2 (x^2 + 3) = 5 \).  
4. Solve for \( x \) in \( \log_4 (x) + \log_4 (x - 3) = 2 \).  
5. What are the properties of logarithms that help simplify equations?  

### **Tip:**  
When solving logarithmic equations, always check for **extraneous solutions** by substituting the final value back into the original equation. Logarithms are **undefined for negative arguments**.

Learn how to solve logarithmic equations by converting them into exponential form and solving for x. This problem involves logarithms with a base of 5, and covers key concepts like logarithmic-to-exponential conversion and solving for variables. Suitable for students in Grades 9-11.

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