Logarithms Notes for SSC Mathematics

A logarithm is the power to which a base must be raised to get a number. If a^x = N, then log_a N = x. Logarithm questions in SSC are based on a few laws and need quick calculation.

Laws of Logarithms

Important Values (base 10)

• log 2 = 0.3010, log 3 = 0.4771, log 5 = 0.6990, log 7 = 0.8451.
• log 10 = 1, log 100 = 2 and log 1000 = 3.
• log(10) = log 2 + log 5 = 1.

Characteristic and Mantissa

For a number such as 345, log 345 = 2.5378. The part before the decimal (2) is the characteristic and the decimal part is the mantissa. The characteristic of a number greater than 1 is the number of digits before the decimal point minus 1.

Solved Example

Find log₂ 32. Since 2⁵ = 32, log₂ 32 = 5. Using the change of base: log 32/log 2 = 5 log 2/log 2 = 5.

Quick Tips

• Convert the number to a power of the base wherever possible.
• log(a + b) cannot be broken into log a + log b.
• Remember log 2 and log 3 for most calculations.
• The logarithm of a negative number or zero is not defined.

Quick Revision Points

• log(mn) = log m + log n.
• log(m/n) = log m − log n.
• log(m^n) = n log m.
• log_a a = 1.
• log_a 1 = 0.
• Change of base: log_a b = log b / log a.

Practice Questions With Answers

1. Find log base 2 of 8.
   Answer: 3
2. Find log base 10 of 100.
   Answer: 2
3. Find log 2 + log 5 (base 10).
   Answer: 1
4. What is the value of log base a of 1?
   Answer: 0
5. If log base 3 of x = 2, find x.
   Answer: 9
6. Evaluate log 8 / log 2.
   Answer: 3
7. Find log base 4 of 64.
   Answer: 3
8. Find log base 10 of 1000.
   Answer: 3

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Mathematics notes page.

Frequently Asked Questions

What is a logarithm?

The power to which the base is raised to get the number.

What is the value of log 1?

Zero.

What is the product law?

log(mn) = log m + log n.

What is the change of base formula?

log_a b = log b / log a.

What is the log of a negative number?

Not defined in real numbers.

What are common logarithms?

Logarithms to base 10.

What are natural logarithms?

Logarithms to base e.

What is the characteristic?

The integral part of a logarithm.

What is the mantissa?

The decimal part of a logarithm.

How to practise?

Solve 10 log problems daily using the laws.