If 

log Subscript 5 Baseline x equals 2log5x=2​, 

find the value of x without a calculator.

Given the equation \( \log_5 x = 2 \), we need to find the value of \( x \).

### Step-by-Step Solution:

1. **Understand the Logarithmic Equation:**
   \[
   \log_5 x = 2
   \]
   This equation means that the base \( 5 \) raised to the power of \( 2 \) gives \( x \).

2. **Rewrite the Equation in Exponential Form:**
   The equation can be rewritten as:
   \[
   x = 5^2
   \]

3. **Calculate the Value of \( x \):**
   \[
   x = 25
   \]

So, the value of \( x \) is \( 25 \).

Would you like to explore further concepts or have more questions about logarithms?

Here are 5 related questions:
1. What is the process to solve logarithmic equations with different bases?
2. How do you solve \( \log_b x = y \) for \( x \) in general?
3. Can you solve \( \log_2 (x+3) = 3 \) for \( x \)?
4. What is the relationship between logarithms and exponents?
5. How can you solve equations that involve natural logarithms (\(\ln\))?

**Tip:** When solving logarithmic equations, always consider rewriting them in exponential form to simplify the solution process.

Learn how to solve the logarithmic equation log base 5 of x equals 2 with a step-by-step solution. This problem involves logarithmic concepts and exponential equations. Suitable for students in Grades 9-12.

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