To express and solve $4^3 = 64$ in logarithmic form, follow these steps:

Step 1: Recall the logarithmic form definition

The general logarithmic form is: $a^b = c \quad \Rightarrow \quad \log_a(c) = b$

Step 2: Rewrite $4^3 = 64$ in logarithmic form

Here, the base $a = 4$, the exponent $b = 3$, and the result $c = 64$. The logarithmic form is: $\log_4(64) = 3$

This states that the logarithm of $64$ to the base $4$ is $3$.

Would you like further clarification or a breakdown of logarithmic properties?

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Related Questions:

1. How can logarithmic forms be used to solve exponential equations in general?
2. What are some real-world applications of logarithms in science or engineering?
3. How do you evaluate logarithms without a calculator?
4. What is the relationship between logarithms and exponentiation?
5. How would you graph $\log_4(x)$ and $4^x$ on the same coordinate plane?

Tip: Always remember that the base in logarithms must be positive and not equal to 1.