## 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

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

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 Quote on Mathematics

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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 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.”solving logarithmic equations
solving logarithmic equations 