Math Problem Statement
log base 3 power 4 + log base 3 power 15 - log base 3 power 20
Solution
To solve the expression:
we can use the properties of logarithms. Specifically:
- The product rule: .
- The quotient rule: .
Step 1: Combine the first two terms
Using the product rule on :
Step 2: Apply the quotient rule
Now, we substitute this result into the original expression:
Step 3: Simplify the fraction
So, the expression becomes:
Step 4: Evaluate
Since (because ), we find:
Final Answer
Would you like further details on logarithmic properties or have any questions?
Here are some related questions to explore:
- What is the result of ?
- How would the answer change if we used a different base for the logarithms?
- How does the change of base formula apply to logarithmic expressions?
- What happens when the expression includes square roots or exponents in logarithmic terms?
- Can we simplify expressions like in general form?
Tip: Remember, combining logarithmic terms by multiplication or division can simplify complex logarithmic expressions!
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Math Problem Analysis
Mathematical Concepts
Logarithms
Logarithmic Properties
Formulas
Product Rule for Logarithms: log_b(a) + log_b(c) = log_b(a * c)
Quotient Rule for Logarithms: log_b(a) - log_b(c) = log_b(a / c)
Theorems
Logarithmic Properties
Suitable Grade Level
Grades 10-12
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