To write the equation \( 64^{-\frac{2}{3}} = \frac{1}{16} \) in logarithmic form, follow these steps:

1. Recall the logarithmic form: If \( a^b = c \), then the logarithmic form is \( \log_a(c) = b \).
2. Identify the base \( a \), the exponent \( b \), and the result \( c \) in the given equation:

   - Base \( a = 64 \)
   - Exponent \( b = -\frac{2}{3} \)
   - Result \( c = \frac{1}{16} \)

So, the logarithmic form of the equation is:

\[
\log_{64}\left(\frac{1}{16}\right) = -\frac{2}{3}
\]

Would you like more details or have any questions?

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Here are 8 related questions:

1. What is the logarithmic form of \( 81^{-1/2} = \frac{1}{9} \)?
2. How do you convert a logarithmic equation back to its exponential form?
3. What are the properties of logarithms that simplify calculations?
4. What is the value of \( \log_{100}(10) \)?
5. How do you calculate \( \log_b(xy) \) using logarithm rules?
6. What is the change of base formula for logarithms?
7. How would you solve \( 10^{x} = 1000 \) using logarithms?
8. What is the inverse function of the logarithmic function?

**Tip:** Always check the base of the logarithm and ensure that it matches the corresponding exponential equation when converting between forms.

Learn how to write the logarithmic form of the equation 64^-2/3 = 1/16 step-by-step. Understand the concept of logarithms and exponential equations. Suitable for high school students.

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