Write the equation in equivalent logarithmic form.
Upper VequalsUpper H Superscript k

To convert the equation \( V = H^k \) into its equivalent logarithmic form, follow these steps:

1. Start with the equation: \( V = H^k \).
2. Apply the logarithm to both sides, typically using the base \( H \), because \( H^k \) suggests the use of base \( H \).
3. This gives: \( \log_H(V) = \log_H(H^k) \).
4. Since \( \log_H(H^k) = k \), the equation simplifies to: 

\[
\log_H(V) = k
\]

So, the equivalent logarithmic form of the equation \( V = H^k \) is:

\[
\log_H(V) = k
\]

Would you like more details or have any questions about this? Here are some related questions you might consider:

1. What is the process for converting a logarithmic equation back into exponential form?
2. How does the change of base formula apply to logarithmic equations?
3. How do logarithmic scales work in practical applications?
4. What is the relationship between logarithms and exponents in calculus?
5. How do you solve logarithmic equations with different bases?

**Tip:** When converting between exponential and logarithmic forms, remember that the logarithm essentially answers the question: "To what power must the base be raised, to yield a specific number?"

Learn how to convert the equation V = H^k into its equivalent logarithmic form using logarithm base change and properties. This problem involves fundamental concepts in logarithms and exponents. Suitable for students in Grades 9-12.

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