## Simplifying Logarithms

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 3

= log ₃ (3³ x 3⁶)

= log ₃ (3)

= 9 log ₃ 3

= 9 (1)

=

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 36 + 2 log 4 - 3 log 4

Solution :

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

= log √36 + log ₉ 4² - log ₉ 4³

= log √(6 x 6) + log ₉ 16 - log ₉ 64

= log 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: