One can easily expect questions on simple applications of logarithms in CAT and other entrance exams. In this article, we will be covering the basic concept of logarithm and various rules that one must be aware of to solve logarithm based questions.

In simple words, it represents the power to which a number must be raised.

For example: log_{2 }8 = 3 as 2^{3} = 8.

The value of logarithm consists of two parts. The integral part is called **the Characteristic** and the decimal part is called **the Mantissa**.

For example, log 70 = 1.845

In 1.845, the Integral part (characteristic) is 1 and the decimal or fractional part (mantissa) is 0.845.

For logarithms, we consider only positive numbers as logarithm for negative numbers is not defined. Also, assume that a, b ≠ 1.

**Logarithm rules:**

1. log_{a} a = 1

2. log_{a} (x^{p}) = p log_{a} x

3. log_{a} a^{x} = x log_{a} a = x

4. a^{(log}a^{x)} = x

5. log_{a} (xy) = log_{a} x + log_{a} y

6. log_{a} (x/y) = log_{a} x – log_{a} y

7. To change the base log_{a }x = log_{b} x / log_{b} a

8. log_{a} (1/x) = – log_{a} x

9. log 1 = 0

10. log_{a} (x + y) ≠ log_{a} x + log_{a} y (commonly made mistake)

11. log_{a} (x – y) ≠ log_{a} x – log_{a} y (commonly made mistake)

If you know these rules, you can solve any question from logarithms quickly. Don’t leave a question just because it has been complicated by using logarithms. Study these rules and see if you can apply them to different problems. All the best!

The article on advanced questions on logarithms can be viewed by clicking on this link.

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