Q 40. - Precalculus Enhanced with Graphing Utilities

Question

Find the domain of the function.

$H\left(x\right)={\log }_5\left(x^3\right)$

Step-by-Step Solution

Answer

The domain of the given function $H\left(x\right)$is $\left(0,\infty \right)$.

Step 1. Given information

A logarithmic function is given as $H\left(x\right)={\log }_5\left(x^3\right)$.

Step 2. Formula Used

The domain of the logarithmic function $f\left(x\right)={\log }_a\left(x\right)$ is determined by $x>0$. 

Step 3. Finding The Domain

The function is $H\left(x\right)={\log }_5\left(x^3\right)$

Now, for the domain,

$x^3>0$

On solving

$x>0$

The required domain of $H\left(x\right)$, using

interval notation, is $\left(0,\infty \right)$.