# LOG BASIC FORMULA

Log basic formula are those formulas which are used to solve exponential problems. There are several exponents formulas that are used to the exponential unknown value of variables. The log is a type of another mathematical operation. Although, it is useful in exponential type equation but can also be helpful in solving many other problems. Moreover, mathematicians and physicians both consider log as an important tool in solving problems. In earlier stages logarithm is considered as just a matter of solving problems based on different bases. But with the passage of time it’s uses evolved and are shown to the word in a very unique manner. Now, most of the experiment based value uses log as their main source for solving unknown.

## The Need for Log Basic Formula

Necessity is the mother of invention. By the invention of the exponential equation and its formulas, mathematicians believe that it is enough to solve all the problems based on power. But when things go out of the box then a problem comes up with no solution at that time. Power-based problems become unsolvable when there is a different base as discussed below.

So, these types of problems are big challenges at that time. This forms the need of discovering some more tools in mathematics. With the introduction of the logarithm, all these needs are now satisfied. In order to make it more useful, some basic formulas are also considered which are mentioned as under.

### Log Basics Formulas

The above-mentioned formulas are some basic formulas used in solving log problems.

**Product rule**: The product of two logs can be written as the sum of both the products. After putting values separately, we can easily find the result. Moreover, the inverse is also true for this rule. That is the sum of two logs can be written as the product of both.

**Division rule**: this is another important rule. It is helpful in solving complex log equations by simplifying it. In this rule, both the term in numerator and denominator are separated with a minus sign. The numerator part is considered as positive and the denominator part is considered as negative. We can find find the resultant value easily. Moreover, the inverse is also true for the same.

**Power rule**: This rule is valid for the power term containing the log. The power is then multiplied with the log value. Power either positive or negative will be multiplied before that log. Although, the inverse is also true.

#### Change of base formula

This is the most important formula in logarithm. With the help of these formulas, we can easily transform the log with different bases. Changing the base and then solving the equation makes it easy for the students. The value of log with base 10 is easy to solve. The log with base e is considered as a natural log. For changing the log, we divide the log with the base log taking a different base. Moreover, The student must know log basic formula for understanding mathematics easily.

Some standard value of log is discussed above. Like values of 0,1,10, 100…etc.

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