Math Problem Statement

log_(10)(40)+\log _(10)(2;5)

Solution

The expression you've provided is:

log10(40)+log10(2;5)\log_{10}(40) + \log_{10}(2;5)

The semicolon ;; in the logarithm argument log10(2;5)\log_{10}(2;5) might indicate a decimal separator commonly used in some European countries, so 2;52;5 can be interpreted as 2.52.5.

This makes the expression equivalent to:

log10(40)+log10(2.5)\log_{10}(40) + \log_{10}(2.5)

Now, we can simplify this using the logarithm property:

log10(a)+log10(b)=log10(a×b)\log_{10}(a) + \log_{10}(b) = \log_{10}(a \times b)

So:

log10(40)+log10(2.5)=log10(40×2.5)\log_{10}(40) + \log_{10}(2.5) = \log_{10}(40 \times 2.5)

Next, multiply 4040 and 2.52.5:

40×2.5=10040 \times 2.5 = 100

Thus:

log10(100)=2\log_{10}(100) = 2

So, the final answer is:

log10(40)+log10(2;5)=2\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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Logarithms
Properties of Logarithms

Formulas

Logarithm property: log(a) + log(b) = log(a * b)

Theorems

-

Suitable Grade Level

Advanced High School