Math Problem Statement
2log 50 + 2 Log 8 - 2 Log 100
Solution
We can simplify the expression using logarithmic properties. Here's the step-by-step solution:
Step 1: Apply the logarithm power rule
The logarithm power rule states that . Let's apply this to each term:
So the expression becomes:
Step 2: Simplify the exponents
Now calculate the squares:
Thus, the expression is now:
Step 3: Apply the logarithm addition and subtraction rules
The logarithm addition rule states , and the subtraction rule states .
First, combine the terms using the addition rule:
Step 4: Perform the multiplication
Calculate :
So the expression becomes:
Step 5: Apply the subtraction rule
Finally, apply the subtraction rule:
Step 6: Simplify the division
Simplify the fraction:
So the final simplified expression is:
Final Answer:
The expression simplifies to .
Would you like more details on any part of this process?
Relative Questions:
- How do you use the change of base formula for logarithms?
- Can you explain the logarithm product rule in detail?
- How do logarithm properties apply to solving logarithmic equations?
- What are the common logarithms and their typical applications?
- How would you expand or condense more complex logarithmic expressions?
Tip: Always remember that logarithms turn multiplication into addition and division into subtraction, which is handy when simplifying expressions.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Logarithmic Properties
Exponentiation
Formulas
Logarithm Power Rule: a log b = log b^a
Logarithm Addition Rule: log a + log b = log (a * b)
Logarithm Subtraction Rule: log a - log b = log (a / b)
Theorems
Properties of Logarithms
Suitable Grade Level
Grades 9-11
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