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To convert these exponential equations into logarithmic form, we will use the logarithmic identity:

\[
\text{If } a^b = c, \text{ then } \log_a(c) = b.
\]

Let’s apply this to each of the given equations:

1. \(5^3 = 125\)
   - This becomes: \(\log_5(125) = 3\).

2. \(10^2 = 100\)
   - This becomes: \(\log_{10}(100) = 2\).

3. \(e^2 = x\)
   - This becomes: \(\ln(x) = 2\), where \(\ln(x)\) is the natural logarithm (base \(e\)).

Would you like more details or have any questions?

Here are some related questions to deepen your understanding:

1. How do you express \(2^5 = 32\) in logarithmic form?
2. What is the logarithmic form of \(7^2 = 49\)?
3. Can you convert \(3^4 = 81\) into logarithmic form?
4. How would you express \(2^x = 16\) in logarithmic terms?
5. What is the logarithmic form of \(x^5 = 3125\)?

**Tip:** Remember, logarithms help to solve for exponents. If you have an equation in the form \(a^x = b\), the logarithmic form helps isolate \(x\) by using the logarithm of \(b\) with base \(a\).

Rewrite the following exponential equations in logarithmic form, whenever possible:
1. 5^3 = 125
2. 10^2 = 100
3. e^2 = x

Learn how to convert exponential equations to logarithmic form with examples such as 5^3 = 125, 10^2 = 100, and e^2 = x. Explore key mathematical concepts like exponents, logarithms, and the logarithmic identity. Suitable for students in Grades 9-12.

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