Question

The domain of the logarithmic function$f\left(x\right)={\log }_{a}x$is _____.

Short answer

The domain of the logarithmic function$f\left(x\right)={\log }_{a}x$is$(0,\infty )$.

Step-by-step solution

Step 1. Given information

Given expression is$f\left(x\right)={\log }_{a}x$

Step 2. Find value of 'x'

Let, $y=f\left(x\right)$

Then,

$y={\log }_{a}x$

omitting logarithm , we have,

$x={a^y}_{}$

Step 3. Find domain

The domain is$(0,\infty )$as the value of$a^y$may$0$at minimum or$\infty$at maximum.

Step 4. Check

The domain $(0,\infty )$is appropriate for the function $f\left(x\right)={\log }_{a}x$