# 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.
Correct Answer is (B). 48

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