The expression you've provided is:

\[
\log_{10}(40) + \log_{10}(2;5)
\]

The semicolon \( ; \) in the logarithm argument \( \log_{10}(2;5) \) might indicate a decimal separator commonly used in some European countries, so \( 2;5 \) can be interpreted as \( 2.5 \).

This makes the expression equivalent to:

\[
\log_{10}(40) + \log_{10}(2.5)
\]

Now, we can simplify this using the logarithm property:

\[
\log_{10}(a) + \log_{10}(b) = \log_{10}(a \times b)
\]

So:

\[
\log_{10}(40) + \log_{10}(2.5) = \log_{10}(40 \times 2.5)
\]

Next, multiply \(40\) and \(2.5\):

\[
40 \times 2.5 = 100
\]

Thus:

\[
\log_{10}(100) = 2
\]

So, the final answer is:

\[
\log_{10}(40) + \log_{10}(2;5) = 2
\]

Would you like more details or have any questions?

Here are some related questions you might find helpful:

1. How can logarithms be simplified using properties?
2. What are the differences between common logarithms and natural logarithms?
3. How does the logarithmic scale apply to real-world scenarios?
4. What is the relationship between logarithms and exponentiation?
5. How do you solve a logarithmic equation with different bases?

**Tip:** Always check the context for symbols like semicolons in mathematical expressions, as they might represent decimal points depending on regional conventions.

Learn how to simplify the logarithmic expression log(10)(40) + log(10)(2.5). Understand the properties of logarithms and how to apply them in mathematical equations. Suitable for advanced high school students and anyone preparing for logarithmic calculations.

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