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Question

What are the conditions under which the logarithm log2x(x2−1) is defined ?


A

x > 0

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B

x > 1

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C

x > 1 and x < -1

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D

x < -1

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Solution

The correct option is B

x > 1


We learn that for a logarithm logba to be defined, the following must be satisfied.
a>0b>0 ; b≠1

Given log expression = log2x(x2−1)2x>0 ; 2x≠1
x>0 ; x≠12 ...(1)

Also x2−1>0
(x−1)(x+1)>0.
This is true when x > 1 or x < -1 ...(2)

Combining (1) and (2) we can say x > 1 is the required condition.


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