1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Greeley [361]
3 years ago
12

Combine into a single logarithm. 3log(x+y)+2log(x-y)-log(x^2 +y^2)

Mathematics
1 answer:
seropon [69]3 years ago
6 0

Answer:

3\log _{10}\left(x+y\right)+2\log _{10}\left(x-y\right)-\log _{10}\left(x^2+y^2\right)=\log _{10}\left(\frac{\left(x+y\right)^3\left(x-y\right)^2}{x^2+y^2}\right)

Step-by-step explanation:

Given the expression

3log\left(x+y\right)+2log\left(x-y\right)-log\left(x^2\:+y^2\right)

solving to write into a single logarithm

3log\left(x+y\right)+2log\left(x-y\right)-log\left(x^2\:+y^2\right)

  • \mathrm{Apply\:log\:rule}:\quad \:a\log _c\left(b\right)=\log _c\left(b^a\right)

3\log _{10}\left(x+y\right)=\log _{10}\left(\left(x+y\right)^3\right)

so

=\log _{10}\left(\left(x+y\right)^3\right)+2\log _{10}\left(x-y\right)-\log _{10}\left(x^2+y^2\right)

  • \mathrm{Apply\:log\:rule}:\quad \:a\log _c\left(b\right)=\log _c\left(b^a\right)

2\log _{10}\left(x-y\right)=\log _{10}\left(\left(x-y\right)^2\right)

so

=\log _{10}\left(\left(x+y\right)^3\right)+\log _{10}\left(\left(x-y\right)^2\right)-\log _{10}\left(x^2+y^2\right)

  • \mathrm{Apply\:log\:rule}:\quad \log _c\left(a\right)+\log _c\left(b\right)=\log _c\left(ab\right)

\log _{10}\left(\left(x+y\right)^3\right)+\log _{10}\left(\left(x-y\right)^2\right)=\log _{10}\left(\left(x+y\right)^3\left(x-y\right)^2\right)

so

=\log _{10}\left(\left(x+y\right)^3\left(x-y\right)^2\right)-\log _{10}\left(x^2+y^2\right)

  • \mathrm{Apply\:log\:rule}:\quad \log _c\left(a\right)-\log _c\left(b\right)=\log _c\left(\frac{a}{b}\right)

\log _{10}\left(\left(x+y\right)^3\left(x-y\right)^2\right)-\log _{10}\left(x^2+y^2\right)=\log _{10}\left(\frac{\left(x+y\right)^3\left(x-y\right)^2}{x^2+y^2}\right)

=\log _{10}\left(\frac{\left(x+y\right)^3\left(x-y\right)^2}{x^2+y^2}\right)

Thus,

3\log _{10}\left(x+y\right)+2\log _{10}\left(x-y\right)-\log _{10}\left(x^2+y^2\right)=\log _{10}\left(\frac{\left(x+y\right)^3\left(x-y\right)^2}{x^2+y^2}\right)

You might be interested in
Give an example how to convert <br> $8.50 multiplied by 8 equal 68
tatuchka [14]
If you're looking for a word problem here's one,

Nichole has $8.50 and she decides to invest it in to a company worth $1,000,000 in a year the company is worth $8,000,000 as the company went up in value so did Nichole's investment, how much was Nichole's Investment worth at the end of that year?

If your'e looking for someone to show the math here's that,

if you take the decimal first and multiply that by 8 you get 4 because 0.5*8=4, then you multiply the whole number and get 64 because 8*8=64, add the two together and you get 68, 64+4=68
6 0
4 years ago
5. What is the probability that a number picked from the set {-4,-3,-2,-1,0,1,2,3,4,5) will be a
tatiyna

Answer:

70%.

Step-by-step explanation:

Rearrange the inequality to isolate x. Start by subtracting 5 from both sides of the inequality:

2\,x + 5 - 5 > 1 - 5,

2\, x > -4.

Divide both sides by 2. (Keep in mind that if the multiplier or divisor is smaller than zero, it will flip the inequality sign.)

x > -2.

There are ten numbers in this set. Only seven of them will satisfy this inequality. Note that the ">" symbol means strictly greater than (while "\ge" means greater than or equal to.) As a result, x = -2 will not count as a solution.

Assume that the number is picked randomly.

\begin{aligned}&\text{Probability of Success} \cr = & \dfrac{\text{Number of Choices that lead to Success}}{\text{Number of all Choices}} \cr =& \dfrac{7}{10} \cr = &0.7 \cr =& 70\% \end{aligned}.

6 0
3 years ago
Evaluate 4 times a number q plus 25 when q = 2
FromTheMoon [43]
Evaluate:
4q + 25
q = 2

4(2) + 25

8 + 25

33

<u><em>answer is 33</em></u>

7 0
3 years ago
Why is it important to use significant digits to round the answer
VARVARA [1.3K]
To get closest to the precise answer
4 0
4 years ago
Solve for h:<br> 7=h/3-6<br><br> -3<br> 3<br> 4 1/3<br> 39
mafiozo [28]

Answer:

h=585

Step-by-step explanation:

if its not right your equation was split up and it was hard to tell the difference between a number and a fraction. sorry.

5 0
3 years ago
Other questions:
  • I need help with this guys
    6·2 answers
  • Please help on #2 ! There is a pic
    7·1 answer
  • Step by step what is 4 (x - 1) -3 (x + 2)
    9·2 answers
  • What is: increase 160 by 30%
    14·1 answer
  • PLZZ HELPPPP MEEEEE WITH THIS QUESTION!!!!!!!!!!
    10·1 answer
  • Help please please guys
    14·2 answers
  • I’m confused.<br> Help plz <br><br><br><br> S
    12·1 answer
  • HELP OR I WILL GET EXPELLED <br> what is brown and sticky
    6·2 answers
  • So, these problems are currently my last two problems. There were two rude people that answered them and didn't actually give me
    9·2 answers
  • Y=6x-11<br> -2x-3y=-7<br> find the solution
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!