# CAT Practice : Exponents and Logarithms

Basic Identities of Logarithms

## Basic identities of Logarithm

Q.9: If log2 4 * log4 8 * log8 16 * ……………nth term = 49, what is the value of n?
1. 49
2. 48
3. 34
4. 24

Choice B. 48

## Detailed Solution

First, the nth term of L.H.S need to be defined by observing the pattern :-
It is log(2n) 2.2n
Given,
log2 4 * log4 8 * log8 16 * ……………log(2n) 2.2n = 49
Whenever solving a logarithm equation, generally one should approach towards making the base same.
Making the base 2:-
log2 4 * $\frac {log_2 8}{log_2 4}$ * $\frac {log_2 16}{log_2 8}$ * ....... $\frac {log_2 2.2^n}{log_2 2^n}$
log(2n) 2.2n = 49
log(2n) 2 + log(2n) 2n = 49
1 + n = 49
n = 48.

## Our Online Course, Now on Google Playstore!

### Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

### Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

## More questions from Exponents and Logarithms

With every extra hour you log in for this topic, it becomes exponentially simpler.