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!