## Simplifying Logarithms

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In this page,simplifying logarithms we are going to see some examples to understand how to simplify logarithms without a calculator. Once you go through the following content deeply you can easily simplify any critical logarithm expressions.Usually those simplification problems can be solved by these four formulas.

**Question 1 :**

**Simplify log ₃ 27 + log ₃ 729**

**Solution :**

Since the bases of both log terms are same,so we can use the product rule to simplify this. That is

= log ₃ 27 + log ₃ 729

= log ₃ 3³ + log ₃ 3⁶

= log ₃ (3³ x 3⁶)

= log ₃ (3⁹)

= 9 log ₃ 3

= 9 (1)

= 9

**Question 2 :**

**Simplify log ****₇ 98 - log ****₇ 14 +** **log ****₇ 343**

**Solution :**

= log ₇ 98 - log ₇ 14 + log ₇ 343

= log ₇ (98/14) + log ₇ 343

= log ₇ (7) + log ₇ 7³

= log ₇ 7 + 3 log ₇ 7

= 1 + 3 (1)

= 1 + 3

= 4

**Question 3 :**

**Simplify (1/2) log **₉** 36 + 2 log **₉** 4 -** **3** **log **₉** 4**

**Solution :**

= (1/2) log ₉ 36 + 2 log ₉ 4 - 3 log ₉ 4

= log ₉ √36 + log ₉ 4² - log ₉ 4³

= log ₉ √(6 x 6) + log ₉ 16 - log ₉ 64

= log ₉ 6 + log ₉ 16 - log ₉ 64

= log ₉ (6 x 16) - log ₉ 64

= log ₉ 96 - log ₉ 64

= log ₉ (96/64)

= log ₉ (24/16)

= log ₉ (6/4)

= log ₉ (3/2)

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simple.”simplifying logarithms simplifying logarithms