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 $a$.