https://file.aiquickdraw.com/mathbot/file/1725469458940mcbjomqw.jpg

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.

Learn how to simplify the logarithmic expression log(10^a / 10^b) with a detailed step-by-step solution. This problem covers key concepts in logarithms and exponents, including the logarithm power rule and exponent subtraction rule. Suitable for students in Grades 9-11.

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