Logarithms are useful for business calculations involving exponential functions. A logarithm represents the power to which a fixed number, called the base, must be raised to produce a given number. For example, the logarithm of 1000 to base 10 is 3, written as log10 1000 = 3 or log 1000 = 3. Logarithms allow solving problems like calculating interest rates or number of years to double an investment through exponentiation, done more easily with logarithms than through long arithmetic. Examples show calculating a 12.25% interest rate and that it takes 6.11 years for money to double at 12% interest. Logarithms are widely used in financial institutions for simplifying complicated calculations.

1. Logarithms In
Business
The use of Logarithms in mathematical terms of business

2. What is Logarithm ?
A quantity representing the power to which a fixed number
must be raised to produce a given number. The “fixed number”
is also known as the “Base”.
Here we use shortcuts to exponentials for speedy calculations.
Logarithm(log) of a number to given base is the power or
exponent to which the base must be raised in order to produce
that number.
For example , the logarithm of 1000 to base 10 is 3.
It can be written as : log10 1000 = 3 ;
Usually we use the base of 10, so we can write :
log 1000 = 3.

3. SolvingInterestrate and the numberof year
involvedby usinglogarithm:
• Q: Deposit money grows double in 6 years in a bank, at the interest rate of “I”. Find the value of I .
Soln: Let,
Deposit Money = P
So, Future value = 2P (as per the condition)
Number of years, N = 6
Rate of Interest, I = ?
We Have,
2P = P(1+I)6
 2 = (1+I)6
 log 2 = log (1+I)6
 Log 2 = 6 log(1+I)
 6log (1+I) = log2
 log (1+I) = 0.301029995/ 6
 log (1+I) = 0.050171666
 (1+I) = Antilog 0.050171666
 (1+I) = 1.1225
 I= 1.1225-1
 I = 0.1225 or 12.25%;
So the rate of interest is 12.25%.

4. • Q: A bank takes “ N “ numbers of years to make the money double at interest rate of 12%. Find the
Value of “N”.
• Soln :
• Let ,
Present Value = P
Future Value = 2P
So,
2P = P (1+i)N
 2P = P(1+0.12)N
 2 = (1.12)N
 log 2 = log (1.12)N
 log 2 = N log (1.12)
 N = log2/log(1.12)
 N= 6.11;
So , the Bank takes 6.11 years to make the money double.

5. Conclusion
• The examples showed above are the simple application of
logarithm in business. More complicated and long calculations
are solved with the help of logarithm in financial intuitions
ease.
• If we consider the problem shown above and try to solve
them with arithmetic method that could be a very long
calculation and there was a chance to make mistake with that.
By using logarithm , we solve it quite easily and almost
without ant error. This is the reason why logarithm are widely
popular in terms of complicated calculations in business and
financial calculation.