Which diagram BEST represents the relationship among integers, rational numbers, and whole numbers?

Mathematics

1 answer:

Ronch [10]3 years ago

8 0

Answer:

The correct option is;

Step-by-step explanation:

By the representation of numbers in a figurative for, we have;

1) Th rational numbers that can be expressed in the form a/b, where a and b are real numbers

2) The integers are the direct subset of the set of rational numbers and are displayed in he next larger ellipse in the figure

3) The whole numbers are the direct subset of the set of integers.

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Rewrite the following as a single logarithm. Please show ALL work!<br><br> 4logx+logy-1/2logz

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Answer:
$\log\left(\frac{x^4y}{\sqrt{z}}\right)$
(if this font is too small then try zooming in, or you can check out the attached image which shows the answer in bigger font)

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Work Shown:

I'm going to use the following rules
Rule 1: log(x)+log(y) = log(x*y)
Rule 2: log(x)-log(y) = log(x/y)
Rule 3: y*log(x) = log(x^y)
Rule 4: x^(1/2) = sqrt(x) ... where 'sqrt' stands for 'square root'

Using those rules, we get...
4*log(x)+log(y) - (1/2)*log(z)
log(x^4)+log(y) - log(z^(1/2)) <<-- using rule 3
log(x^4)+log(y) - log(sqrt(z)) <<-- using rule 4
log(x^4*y) - log(sqrt(z)) <<-- using rule 1
log[ (x^4*y)/(sqrt(z)) ] <<-- using rule 2