$What are the conditions under which the$
$logarithm$ $l o g_{2 x} (x - 1)$ is defined ?

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Solution

We have learned that for a logarithm $l o g_{b} a$ to be defined, the following must be satisfied.

a > 0
b > 0

Given log expression = $l o g_{2 x} (x - 1)$
$2 x > 0$
$x > 0$ ...(1)

Also $(x - 1) > 0$
$\Rightarrow x > 1$ ...(2)

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

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