do the same for $$ -2\log_{b}\left(b\right) $$$$  $$

Given the expression $-2\log_b(b)$, let's simplify it.

We know that:

\[
\log_b(b) = 1
\]

This is because any logarithm where the base and the argument are the same equals 1. Therefore, we can substitute:

\[
-2\log_b(b) = -2 \times 1 = -2
\]

So, the simplified expression is:

\[
-2\log_b(b) = -2
\]

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:
1. What is the value of $3\log_b(b)$?
2. How can you express $\log_{b^2}(b)$ in terms of $\log_b(b)$?
3. What does $\log_b(b^n)$ simplify to?
4. How does the expression $\log_b(b^{-1})$ simplify?
5. Can $\log_b(1)$ be expressed in terms of $\log_b(b)$?

**Tip:** Recognizing standard logarithmic identities, such as $\log_b(b) = 1$, can help simplify complex expressions quickly and accurately.

Explore how to simplify the expression -2log_b(b) step-by-step. Understand the logarithmic identity $ \log_b(b) = 1 $ used in this solution. Suitable for high school students studying logarithms.

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