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
faltersainse [42]
3 years ago
5

Expand using the properties and rules for logarithms

Mathematics
1 answer:
malfutka [58]3 years ago
7 0

Consider expression \log_{\frac{1}{2}}\left(\dfrac{3x^2}{2}\right).

1. Use property

\log_a\dfrac{b}{c}=\log_ab-\log_ac.

Then

\log_{\frac{1}{2}}\left(\dfrac{3x^2}{2}\right)=\log_{\frac{1}{2}}3x^2-\log_{\frac{1}{2}}2.

2. Use property

\log_abc=\log_ab+\log_ac.

Then

\log_{\frac{1}{2}}\left(\dfrac{3x^2}{2}\right)=\log_{\frac{1}{2}}3x^2-\log_{\frac{1}{2}}2=\log_{\frac{1}{2}}3+\log_{\frac{1}{2}}x^2-\log_{\frac{1}{2}}2.

3. Use property

\log_ab^k=k\log_ab.

Then

\log_{\frac{1}{2}}\left(\dfrac{3x^2}{2}\right)=\log_{\frac{1}{2}}3+\log_{\frac{1}{2}}x^2-\log_{\frac{1}{2}}2=\log_{\frac{1}{2}}3+2\log_{\frac{1}{2}}x-\log_{\frac{1}{2}}2.

4. Use property

\log_{a^k}b=\dfrac{1}{k}\log_ab.

Then

\log_{\frac{1}{2}}\left(\dfrac{3x^2}{2}\right)=\log_{\frac{1}{2}}3+2\log_{\frac{1}{2}}x-\log_{\frac{1}{2}}2=\log_{\frac{1}{2}}3+2\log_{\frac{1}{2}}x-\log_{2^{-1}}2=\\ \\=\log_{\frac{1}{2}}3+2\log_{\frac{1}{2}}x+\log_22=\log_{\frac{1}{2}}3+2\log_{\frac{1}{2}}x+1.

Answer: correct option is B.

You might be interested in
2(3v - 8) <br> please help xxxxxxxxxxxxxxxxxxxxxxxxxx
WINSTONCH [101]

Answer: 6 v − 16

Step-by-step explanation:

7 0
3 years ago
80 Hundreds = ____ Thousandths
allsm [11]
The answer would be 0.8, because 800 hundreds go into 8 thousandths, but there is only 80 hundreds, so the answer is 0.8 thousandths.
Answer: 0.8 thousandths

PLZ MARK MINE THE BRAINLIEST ANSWER!!!
3 0
3 years ago
Find the sum and express it in simplest form. (ab+4a-6)+(ab+6)
riadik2000 [5.3K]
= 2ab + 4a + 6 - 6

= 2ab + 4a

you can factor this  to 2a(b + 2)
3 0
3 years ago
Read 2 more answers
A town has a population of 50,000. it’s rate increase is 8% every 6 months. find the population after 4 years
Ainat [17]
82,000 bc 8% of 50,000 is 4000 and 4000 times 8 is 32,000 + 50000
6 0
2 years ago
Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below.
agasfer [191]

Answer:

Class Boundary = 1 between the sixth and seventh classes.

Step-by-step explanation:

              Lengths (mm)                   Frequency

1.                  140 - 143                                  1

2.                 144 - 147                                 16

3.                 148 - 151                                 71

4.                 152 - 155                              108

5.                 156 - 159                               83

6.                 160 - 163                                18

7.                  164 - 167                                 3

The class boundary between two classes is the numerical value between the starting value of the higher class, which is 164 for the 7th class in this case, and the ending value of the class of the lower class, which is 163 for the 6th class in this case.

Therefore the class boundary between the sixth and seventh classes

= 164 - 163  = 1

Therefore Class Boundary = 1.

It can be seen that class boundary for the frequency distribution is 1.

If we take the difference between the lower limits of one class and the lower limit of the next class then we will get the class width value.

Therefore, Class width,

w = lower limit of second class - lower limit of first class

   = 144 - 140

   = 4

7 0
3 years ago
Other questions:
  • A line with a slope of 1 passes through (-5,-5). Write the equation of the line in general form.
    10·1 answer
  • What is the length of segment CD
    12·1 answer
  • The temperature dropped 1.8 degrees celcuis each hour for 4 1/2 hours starting from 8 p.m. if the temperature was 4.6 degrees ce
    10·2 answers
  • Solve the inequality, -4 less than 4(6y-12)-2y
    8·1 answer
  • 21 x 2/5 ninths math problem
    11·2 answers
  • BRAINLIEST FOR RIGHT ANSWER!!! The graph shows two lines, A and B. (IMAGE BELOW) How many solutions are there for the pair of eq
    8·1 answer
  • Gets brainilist!!!!!!!what is the absoulute value of -4.5 and what is the absoulute value of 1
    5·2 answers
  • An artist is selling children's crafts. Necklaces cost $3.25 each, and bracelets cost $2.50 per each. The artist plan to have a
    15·1 answer
  • Please help me i love u so much
    12·1 answer
  • PLEASE HELP! SO CONFUSED! 25 POINTS!!
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!