Question

Find the domain of the function.

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

Short answer

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

Step-by-step solution

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 $\left(0,\infty \right)$.