**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.

To Find: Use logarithmic properties to simplify the given expressions.

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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Question

**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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