You can use the definition of **logarithm **and the fact that a **positive **number raised to any **power** will always stay bigger than 0.

The **domain **of the given **function **is {x | x > 1 and a real number }

The **range **of the given function is (set of real numbers)

<h3>What is the definition of logarithm?</h3>

If a is raised to power b is resulted as c, then we can rewrite it that b equals to the **logarithm **of c with base a.

Or, symbolically:

Since c was the result of a raised to power b, thus, if a was a **positive** number, then a raised to any **power **won't go less or equal to zero, thus making c > 0

<h3>How to use this definition to find the domain and range of given function?</h3>

Since log(x-1) is with **base **10 (when base of log isn't specified, it is assumed to be with base 10) (when log is written ln, it is **log **with base e =2.71828.... ) thus, we have a = 10 > 0 thus the input x-1 > 0 too.

Or we have:

x > 1 as the **restriction**.

Thus **domain **of the given function is {x | x > 1 and a real number }

Now from **domain**, we have:

(log(x-1) > -infinity since log(0) on right side have arbitrary **negatively **large value which is denoted by -infinity)

Thus, **range** of given **function** is whole real number set (since all finite real **numbers **are bigger than negative infinity)

Thus, the **domain **of the given **function **is {x | x > 1 and a real number }

The **range **of the given function is (set of real numbers

Learn more about **domain **and **range **here:

brainly.com/question/12208715