https://r2.erweima.ai/mathbot/image/1725673949467gqx7cvpc.jpg

The expression provided in the image is:

\[
2 \log_2 \left( 3 \left( \frac{32}{3} \right) \right)
\]

Let’s simplify this step by step.

### Step 1: Simplify inside the parentheses
First, simplify the inner part \( 3 \left( \frac{32}{3} \right) \):
\[
3 \times \frac{32}{3} = 32
\]

### Step 2: Apply the logarithm
Now we have:
\[
2 \log_2 (32)
\]

Since \( \log_2 (32) \) is asking for the power to which 2 must be raised to get 32, and \( 32 = 2^5 \), we know:
\[
\log_2 (32) = 5
\]

### Step 3: Final calculation
Now we multiply by 2:
\[
2 \times 5 = 10
\]

Thus, the simplified expression is:
\[
\boxed{10}
\]

Would you like further details or have any questions?

---

Here are 5 related questions for further practice:
1. How do you simplify \( \log_2 (64) \)?
2. What is \( \log_2 \left( \frac{1}{4} \right) \)?
3. If \( \log_b(x) = y \), what is \( x \) in terms of \( b \) and \( y \)?
4. How can you express \( \log_2(8 \times 4) \) as a sum of two logarithms?
5. What is the value of \( \log_2(1024) \)?

**Tip**: To quickly evaluate logarithms like \( \log_2 \), recognize powers of 2 (e.g., \( 2^5 = 32 \)).

Simplify the expression: 2 * log2(3 * (32 / 3))

Learn how to simplify the expression 2 * log2(3 * (32 / 3)) step by step. This problem involves logarithmic properties, including simplification and powers of 2. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation