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: 

It subtracts sadness and adds happiness in our life.    

It divides sorrow and multiplies forgiveness and love.

Some people would not be able to accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When our people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

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