Math Problem Statement
number 30
log_3(1/9) - 3log_3(3)
Solution
Let's solve problem 30 from the image step by step.
Problem:
Step 1: Apply logarithmic properties.
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Simplify .
We know that . Using the logarithmic property , we get: Since , this simplifies to:
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Simplify .
From the logarithmic property , and knowing that , we get:
Step 2: Combine the results.
Now, we can subtract the two terms:
Final Answer:
Would you like more details on any step, or do you have any questions?
Here are 5 related questions to deepen your understanding:
- How would you evaluate using properties of logarithms?
- Can you simplify in general terms?
- What happens when you evaluate ? Why is it always 0?
- How can you use the change-of-base formula to evaluate logarithms with bases other than 10 or ?
- How would you simplify for any ?
Tip:
Whenever you see a logarithm of a fraction, try expressing the fraction in terms of powers of the base, as this often simplifies the problem quickly.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Exponents
Formulas
log_b(a^n) = n log_b(a)
log_b(b) = 1
Theorems
Logarithmic properties
Exponent rules
Suitable Grade Level
Grades 10-12