3. Use log properties to simplify. Your answer should not include any logs or negative exponents. SHOW ALL STEPS a) log2(2 log3(9)) b) log 3 – log 60 + log 2 (watch your signs here, note that minus sign is NOT distributed) c) 6log6 11-2 log, 5 (be careful here, simplify entire exponent first)
3. Use log properties to simplify. Your answer should not include any logs or negative exponents. SHOW ALL STEPS a) log2(2 log3(9)) b) log 3 – log 60 + log 2 (watch your signs here, note that minus sign is NOT distributed) c) 6log6 11-2 log, 5 (be careful here, simplify entire exponent first)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Logarithm Simplification Problems**
### 3. Use log properties to simplify. Your answer should not include any logs or negative exponents.
**SHOW ALL STEPS**
#### a) \( \log_2 (2 \log_3 (9)) \)
#### b) \( \log 3 - \log 60 + \log 2 \)
*(watch your signs here, note that the minus sign is NOT distributed)*
#### c) \( 6^{\log_6 11 - 2 \log_6 5} \)
*(be careful here, simplify entire exponent first)*
---
**Explanation:**
To simplify these logarithmic expressions, make sure you are familiar with key logarithmic properties such as the product rule, quotient rule, power rule, and change of base formula.
When solving these problems, write down each step to avoid errors, especially watch for the sign and ensure correct application of the rules without distributing improperly.
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