The problem is asking to convert exponential equations into logarithmic form. Let's go through each part.

Part (a)

The given equation is: $4^5 = 1024$ In logarithmic form, an equation $a^x = b$ can be written as $\log_a b = x$.

Applying this to $4^5 = 1024$: $\log_4 1024 = 5$ So:

• $A = 1024$
• $B = 5$

Part (b)

The given equation is: $10^{-2} = 0.01$ Applying the same logic, we can rewrite $10^{-2} = 0.01$ as: $\log_{10} 0.01 = -2$ So:

• $C = 0.01$
• $D = -2$

Summary of Answers

• (a) $A = 1024$, $B = 5$
• (b) $C = 0.01$, $D = -2$

Would you like further details on logarithmic conversions or have any questions?

Related Questions

1. How do you convert any exponential equation into logarithmic form?
2. What is the general rule for changing the base in logarithmic expressions?
3. Why is $\log_{10} 0.01 = -2$? How does the negative exponent affect the calculation?
4. What are other ways to simplify logarithmic expressions?
5. How does understanding logarithmic form help in solving exponential growth problems?

Tip: Remember that logarithms answer the question, "To what power must the base be raised, to yield a specific number?"