Logarithm Sum

Introduction to the logarithm sum :

In the mathematics, the logarithmic number is associated with the unsigned (positive) number to the known base is power or the exponent to which the base must be increased in the order to produce that the number. The logarithm sum is the sum of the individual log values of the variables. The logarithm sum is used to solve the very complex problems. A logarithmic is used in the following applications such as physics, computer, chemistry, economics, astronomy, statistics and engineering.

Formula for the Logarithm Sum:

The logarithmic equation of x to the base b is represented in the form of log b(x) .It describes the number is x, the base is b and an exponent value is y means the logarithmic equation is written as,

`x=b^y` ,  taking log on both sides ,so the equation is `y=log_b (x).`

`log(a)+log(b)+log(c)=log(abc)`

The above formula is used to easily find the logarithm sum of the given values.The varies bases are used in the following types of logarithmic numbers such that base 10 for a common logarithmic equation, e for a natural logarithmic equation, and 2 for a binary logarithmic equation.

Logarithmic Rule:
`log(a/b)=log(a)-log(b)`

`log_b(a)=1/(log_a (b))`

`log _a (a)=1`

`log_(x)1=0`

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Example 1 for Logarithm Sum:

Find the value of the logarithm sum` log 4+log 5+log 6`

Solution:

Given,

`log 4+log 5+log 6=log(4xx5xx6)` [using the logarithm sum rule that is `log a+log b=log(ab)`

=`log (120)`

The answer of the logarithmic equations is `log 120.`

Examples 2 for logarithm sum:

Find the value of the logarithm sum of log 12 using the following values l`og 2=0.3010 and log 3=0.4771.`

Solution:

Given,

`Log 12=log(2xx2xx4)=log 2+log 2+log 3`

Substitute these values `log 2=0.3010 and log 3=0.4771`

`log 12=0.3010+0.3010+0.4771=1.0791`                         

The answer of the logarithmic equations is `log 12= 0.4771`

Example 3 for logarithm sum:

Find the value of the logarithm sum `log 126`

Solution:

Given,

`log 126=log(21xx6)=log(7xx3xx2xx3)`

` =log 7+log 3 +log 2+log 3.`

The answer of the logarithmic equations is `log 7+log 3 +log 2+log 3.`