The expression in the image is:

$\log\left(\frac{10^a}{10^b}\right)$

To simplify this expression, we can follow these steps:

Step 1: Simplify the Fraction Inside the Logarithm

The expression inside the logarithm can be simplified using the property of exponents:

$\frac{10^a}{10^b} = 10^{a-b}$

Step 2: Apply the Logarithm Rule

Use the logarithm rule $\log_b(x^n) = n \cdot \log_b(x)$:

$\log\left(10^{a-b}\right) = (a-b) \cdot \log(10)$

Step 3: Simplify Further

Since $\log(10)$ is 1 (for logarithms with base 10):

$(a-b) \cdot 1 = a - b$

So, the expression simplifies to:

$\log\left(\frac{10^a}{10^b}\right) = a - b$

Would you like any further details on this solution, or do you have any other questions?

Here are five questions related to this topic:

1. How do logarithmic properties simplify complex expressions?
2. What are the key logarithm rules you should remember?
3. How does changing the base of a logarithm affect its value?
4. What are some practical applications of logarithms in real-world problems?
5. How can you apply logarithms to solve exponential equations?

Tip: Always double-check if the base of the logarithm matches the base of the exponent when simplifying expressions.