Question

$\text{What are the conditions under which the}$
$\text{logarithm}$ $lo{g}_{2x}(x-1)$ is defined ?

• A. $x>0$
• B. $x>1$
• C. $x>1$ and $x<-1$
• D. $x<-1$

Answer 1

The correct option is B

$x>1$

We have learned that for a logarithm $lo{g}_{b}a$ to be defined, the following must be satisfied.

a > 0
b > 0

Given log expression = $lo{g}_{2x}(x-1)$
$2x>0$
$x>0$ ...(1)

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

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