## Logarithms, Surds and Indices

Theory

"Logarithms, Surds and Indices" is one of the easiest topics in the quantitative section of the CAT exam. Although the number of formulae is high, the basic concepts are very simple to understand and apply. There are no shortcuts to remember and the scope of the questions that can be asked is very limited. The accuracy of answering questions from this section is very high and good students tend to score very well here.

Formula

$$\log_{a}{1} = 0$$$$$\log_{a}{xy} = \log_{a}{x}+\log_{a}{y}$$$ $$\log_{a}{b}^{c} = c \log_{a}{b}$$$$${b}^{\log_{b}{x}} = x$$$ $${x}^{\log_{b}{y}} = {y}^{\log_{b}{x}}$$$$${\log_{a}{\sqrt[n]{b}}} = \frac{\log_{a}{b}}{n}$$$ $${\log_{a}{b}} = \frac{\log_{c}{b}}{\log_{c}{a}}$$$$${\log_{a}{b}}*{\log_{b}{a}}= 1$$$

• Logarithms can be used to quickly find the number of digits in an exponent.
Shortcuts
• $$\frac{1}{\sqrt{N+1}-\sqrt{N}} ={\sqrt{N+1}+\sqrt{N}}$$
• To convert a recurring decimal into a fraction, multiply the decimal by a power of 10.