simplifying logarithmic expressions questions 10







In this page simplifying logarithmic expressions questions 10 we are going to see solution of tenth question.

Question 10

Simplify 2 log 2 + 3 log ₂ 5 -  log ₂ 15 + log ₂ 7

Solution:

Basic idea : Here totally we have four terms out of these three terms have same bases. First we have to combine them by using logarithmic formulas. Then we have to change base of first term as others. 

                     = 2 log 2 + 3 log ₂ 5 -  log ₂ 15 + log ₂ 7

                     = log 2² + log ₂ 5³ -  log ₂ 15 + log ₂ 7

                     = log 4 + log ₂ 125 log ₂ 15 + log ₂ 7

                     =  1 + log ₂ 125 + log ₂ 7 log ₂ 15 

                     = 1 + log ₂ (125 x 7) log ₂ 15 

                     = log ₂ 2 + log ₂ 875 log ₂ 15

                     = log ₂ 2 + log ₂ (875/15)

                     = log ₂ 2 + log ₂ (175/3)

                     = log ₂ (2 x 175)/3

                     = log ₂ (2 x 175)/3

                     = log ₃ (350/3)


Try these questions also

Question 1

Simplify log ₃ 15 - log ₃ 5 + 2 log ₃ 5


Solution

Question 2

Simplify 2 + 2 log₂ 5 - 3 log₂ 3


Solution

Question 3

Simplify 2 log₂ 5 - 3 log₂ 3


Solution

Question 4

Simplify ½ log 36+2 log ₉4-3log ₉ 4


Solution

Question 5

Simplify log 8log ₅ (1/1000)


Solution

Question 6

Simplify

½ log 36 - ⅓ log ₅ 8 + 3 log 2


Solution

Question 7

Simplify 3 + 5 log ₃ 5


Solution

Question 8

Simplify

log ₃ (65/21) + log ₃ (21/13)


Solution

simplifying logarithmic expressions questions 10

Question 9

Simplify

log ₅ 5+log ₅ 20-log ₅24+log ₅ 25 - 3


Solution


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 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 we 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 logarithmic expressions questions 10 simplifying logarithmic expressions questions 10

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