Name the property the equation illustrates.

Mathematics

1 answer:

maria [59]3 years ago

7 0

Answer: Choice C) Commutative Property of Multiplication

The commutative property of multiplication is the idea that you can multiply two numbers in any order to get the same result. So that's why order doesn't matter. The general format is x*y = y*x

For example, 2*3 = 6 and 3*2 = 6 so 2*3 = 3*2

One or both of the numbers can be a fraction.

You might be interested in

What are the domain and range of f (x) = log (x minus 1) 2?.

statuscvo [17]

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 $\mathbb R$ (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:

$a^b = c \implies b = log_a(c)$

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:

$x > 1\\
x-1 > 0\\
log(x-1) > -\infty\\
log(x-1) + 2 > -\infty\\
f(x) > -\infty$ (log(x-1) > -infinity since log(0) on right side have arbitrary negatively large value which is denoted by -infinity)