Q 4. - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

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

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