can you show me log form from exponential

Yes! Logarithmic form and exponential form are two ways to express the same relationship. Here is how they are related:

If you have an exponential equation:  
\[
a^x = b
\]  
it can be rewritten in logarithmic form as:  
\[
\log_a(b) = x
\]

### Explanation
1. \( a \) is the base of the exponent in the exponential form, and it remains the base of the logarithm in the logarithmic form.
2. \( b \) is the result of raising \( a \) to the power of \( x \) in exponential form; it becomes the input to the logarithm.
3. \( x \) is the exponent in the exponential form, and it becomes the output of the logarithmic form.

#### Example:
- Exponential form: \( 2^3 = 8 \)
- Logarithmic form: \( \log_2(8) = 3 \)

Would you like to see more examples or a graph to visualize the relationship?  

### Related Questions:
1. How do you convert between logarithmic and exponential forms in complex cases?
2. What are some real-world applications of logarithms?
3. How do natural logarithms (\( \ln(x) \)) relate to exponential functions?
4. What happens if the base \( a \) is less than 1 in these forms?
5. Can logarithmic and exponential forms be used to solve equations?  

### Tip:
Remember, logarithms are the inverse of exponential functions. They "undo" exponentiation!

Discover the relationship between logarithmic and exponential forms. Learn how to rewrite equations like a^x = b into log_a(b) = x, with examples and step-by-step explanations. Suitable for students in Grades 9-12 studying Algebra.

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