## 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.

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**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

“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