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)

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are:

It subtracts sadness and adds happiness in our life.

It divides sorrow and multiplies forgiveness and love.

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Many people think that the subject math is
always complicated and it exists to make things from simple to complicate. But
the real existence of the subject math is to make things from complicate to
simple.”simplifying logarithms simplifying logarithms