We are given the expression:

\[
\log_2 \left(\frac{1}{y^2}\right)
\]

Let's solve for \( y \).

1. Use the property of logarithms:
\[
\log_2 \left(\frac{1}{y^2}\right) = \log_2(1) - \log_2(y^2)
\]
Since \( \log_2(1) = 0 \), this simplifies to:
\[
\log_2 \left(\frac{1}{y^2}\right) = - \log_2(y^2)
\]

2. Use the power rule of logarithms \( \log_b(a^n) = n \log_b(a) \):
\[
- \log_2(y^2) = -2 \log_2(y)
\]

Therefore, the expression simplifies to:

\[
\log_2 \left(\frac{1}{y^2}\right) = -2 \log_2(y)
\]

To solve for \( y \), we'd need more information, such as the value of the expression or an equation it's equal to. If the question implies setting it equal to something like 0 or another constant, we could proceed from there.

Would you like to set it equal to something to continue solving, or do you have any other questions?

Here are 5 related questions:
1. How do you solve logarithmic equations with exponents inside?
2. What is the relationship between logarithmic and exponential functions?
3. Can logarithms be negative, and what does it mean?
4. How do you expand logarithmic expressions?
5. What happens when you apply logarithms to fractions?

**Tip**: When dealing with logarithms of fractions or powers, break them into simpler components using logarithmic properties to make the solving process easier.

Learn how to solve the logarithmic equation log base 2 of 1 over y squared. This problem involves applying logarithmic properties and the power rule, essential for understanding logarithmic equations. Suitable for advanced high school students.

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