Log table pdf download: Logarithms is a mathematical term which is used to solve mathematical problems and expressions in the form of exponents and powers. Logarithm is defined as the inverse function of the powers or exponents. Logarithm was introduced by John Napier to reduce the calculations and to make calculations easier to handle in short form.

logab: This is the general notation of logarithm. Where it is denoted as the logarithm of b to the base a It is also called “log”. Logarithm is usually seen in the form of log b

In this form base a is automatically considered to be 10 which has no effect on calculations. But in high level mathematical operations the base may be defined as a natural log that is base b=2 which gives a value ≈ 2.731. In case of problem solving there is already given the value of log to be used in solving the problems.

Log deals with large calculations of exponents and makes calculations easier to solve hence there are some formulae of log which are explained below.

logb(mn)=logbm+logbn

Where b, m and n are positive numbers and greater than 0. Because at 0 it will not hold true. This is product rule in logarithm

logb(m/n)=logbm-logbn

Provided that m,n and b should be positive numbers and greater than 0. It is a division/quotient rule.

logb(xn)=nlogbx

In this rule, if there is a degree or power raised on x alone then that power shifts its place and comes in multiply to the log.

logb n √x=(logbx)/n

This is root identity, in which root power acts as a divisor for the log value, leaving the root and its power.

logba=1/(logab)

This is the base change rule, it means if you multiply two logs by interchanging their bases then their product will give you unity.

Apart from these identities there are some basic log values which are very helpful in solving the questions because deriving these usually asked values may be time-consuming.

 Log Values log1 0 log2 0.301 log3 0.477 log4 0.602 log5 0.698 log6 0.778 log7 0.845 log8 0.903 log9 0.954 log10 1

Note that the base of these logs is 10.

These are some important values, sometimes values are already given in School and college level exams but in higher levels of mathematical calculations there might be a need for these values.

### Applications of Logarithms

• In seismology, the Richter scale on which intensity of earthquake is measured uses a log on the base of 10.
• In Chemistry, chemical behavior is examined on the basis of log. pH values are calculated with the help of logarithm.
• In Nuclear researches and nuclear related studies log is used to determine the rate of radioactive decay.
• Financial institutions like banks, loan institutions make the use of logarithms to calculate the time of loan payment or repayment.
• Growth rates like population growth etc are represented with the help of logarithms.
• Logarithms are used in class 12 Mathematics in integration.
• It is also used in deriving formulas and expressions.
• It is also used in celestial observations.

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