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The problem is about converting exponential equations into their logarithmic forms. Let's focus on the first part (a), which asks you to convert \( 4^5 = 1024 \) into logarithmic form.

For exponential expressions of the form \( a^b = c \), the corresponding logarithmic form is \( \log_a(c) = b \).

So for \( 4^5 = 1024 \), the logarithmic form is:
\[
\log_4(1024) = 5
\]

Therefore, \( C = 1024 \) and \( D = 5 \).

It seems that in your question, \( C \) is incorrectly marked. You should fill \( C = 1024 \), and the correct logarithmic expression is:
\[
\log_4(1024) = 5
\]

Would you like to go over the other parts or have further clarifications?

Here are some related questions you might explore:
1. What is the general relationship between exponents and logarithms?
2. How can logarithms help solve exponential equations?
3. What are the common logarithm bases used in practice?
4. How can you calculate logarithms without a calculator?
5. How does changing the base of a logarithm affect the value?

**Tip:** Remember that logarithms are the inverse operations of exponentiation.

Convert the exponential equations into logarithmic form.

Learn how to convert exponential equations into logarithmic form. This problem covers examples like 4^5 = 1024 and explains the inverse relationship between exponents and logarithms, using the formula a^b = c is equivalent to log_a(c) = b. Suitable for students in Grades 9-11.

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