Question

Graph of $y={\log }_{a}x$ ranges between

• A. $(-\infty ,0)$
• B. $(-\infty ,\infty )$
• C. $(0,\infty )$
• D. $(-1,1)$

Answer 1

The correct option is B $(-\infty ,\infty )$

$y={\log }_{a}xy=\frac{\log x}{\log a}\log x=y\log a\log x=\log a^y\Rightarrow x=a^y$

For function in $y$ to be defined

$y\in (-\infty ,\infty )$

So, the range of the function is $(-\infty ,\infty )$.

Hence, option B is correct