https://file.aiquickdraw.com/mathbot/file/1727071176715aeg058o3.jpg

The expression shown in the image is:

\[
3 \log_{10} 2 - \log_{10} 4
\]

Let's solve this step by step.

### Step 1: Simplify the logarithmic terms
- We know that \( \log_{10} 4 \) can be written as \( \log_{10} (2^2) = 2 \log_{10} 2 \).

Thus, the expression becomes:

\[
3 \log_{10} 2 - 2 \log_{10} 2
\]

### Step 2: Combine like terms
Since both terms involve \( \log_{10} 2 \), we can subtract the coefficients:

\[
(3 - 2) \log_{10} 2 = 1 \log_{10} 2
\]

Thus, the simplified expression is:

\[
\log_{10} 2
\]

### Step 3: Approximate value
Using a calculator, we know:

\[
\log_{10} 2 \approx 0.3010
\]

So the value of the expression is approximately \( 0.3010 \).

Would you like more details or have any questions?

### Related Questions:
1. What are the properties of logarithms used here?
2. How do you express logarithms with different bases?
3. What is the general value of \( \log_{10} 2 \)?
4. How does the change of base formula for logarithms work?
5. How would you solve this if it were a natural logarithm instead?

**Tip:** Remember that logarithms turn multiplication into addition and powers into multiplication, making complex calculations simpler!

Learn how to simplify the logarithmic expression 3log10(2) - log10(4) using logarithmic properties. This problem explores the logarithmic power rule and the subtraction rule, suitable for students in Grades 9-11.

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