Math Problem Statement

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

Solution

The given expression is:

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

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. What are the properties of logarithms and how are they used?
  2. How do you solve logarithmic equations?
  3. What is the change of base formula for logarithms?
  4. How do logarithms relate to exponential functions?
  5. How can you graph logarithmic functions?

Tip: Remember that log10(100)=2\log_{10}(100) = 2 because 102=10010^2 = 100. This is a fundamental property of logarithms.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Properties of Logarithms
Exponential Functions

Formulas

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

Theorems

Logarithm Properties

Suitable Grade Level

Grades 10-12