Solving Logarithmic Equations

In this page solving logarithmic equations we are going to see how to solve value for some variables in a logarithmic equation of different bases. First let us start with simple problems.

Question 1 :

Simplify log ₇ (7x + 14) = 3

Solution :

If the log goes that side it will become

           (7x + 14) = 7³

           (7x + 14) = 343

                    7 x = 343 - 14

                    7 x = 329

                       x = 329/7

                       x = 47

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Question 2 :

Simplify log ₃ (7 - x) - log ₃ (1 - x) = 3

Solution :

Since we have two log terms with same base we are going to combine them by using logarithmic formula

  log ₃ (7 - x) - log ₃ (1 - x) = 3

  log ₃ [(7 - x) ÷ (1 - x)] = 3

           (7 - x) ÷ (1 - x) = 3³

           (7 - x)/(1 - x) = 27

                     (7 - x)  = 27 (1 - x)

                       7 - x  = 27 - 27 x

                - x + 27 x = 27 - 7

                        26 x = 20

                            x = 20/26

                            x = 10/13

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Question 3 :

Simplify  2 log ₅ x  = 3 log ₅ 2

Solution :

Since we have two log terms with same base we are going to combine them by using logarithmic formula

               2 log ₅ x  = 3 log ₅ 2

                  log ₅ x²  = log ₅ 2³

                  log ₅ x²  = log ₅ 8

                          x²  = 8

                          x  = √8

                          x  = √(2 x 2 x 2)

                          x  = 2 √2

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• Solving logarithmic equation worksheet

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.”solving logarithmic equations
solving logarithmic equations