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
25% of 60 to 40% of 30<br> &gt;, &lt; or =
Travka [436]

You can reduce the percentages to fractions:

25\% = \dfrac{25}{100} = \dfrac{1}{4}

40\% = \dfrac{40}{100} = \dfrac{2}{5}

So, we have

25\% \text{ of } 60 = \dfrac{1}{4}\cdot 60 = 15

40\% \text{ of } 30 = \dfrac{2}{5}\cdot 30 = 12

5 0
2 years ago
Which expression simplifies to 8x^5?
tamaranim1 [39]

Answer:

32768x^5

Step-by-step explanation:

8 0
2 years ago
Write a linear inequality in two variables that has (-1, 3) as a solution but does not have (4,0) as a solution.
Stels [109]

Answer:  y ≤ -x + 2

<u>Step-by-step explanation:</u>

There are an infinite number of possible solutions.

Plot the two points, draw any line between them such that the two points are NOT connected, then choose the inequality symbol that shades (-1, 3).

Here is one solution that satisfies the requirements.   y ≤ -x + 2

Here is another: y < -x + 3

And another: y > x + 3

And one more: y ≥ x + 4

3 0
3 years ago
Helpppppp pleaseeeeeee
NeX [460]

Answer: b)

Step-by-step explanation:

You can rule out A) and C), because you have to find area (no adding.)

To do this problem, you can individually multiply the estimated hieght and

width by 3 and then multiply together.

This is because there are 3 walls that each are 9 3/4 tall and 14 1/4 wide. To find total height and width, multiply by 3. Then find total area (lxw)

9 3/4 rounds to 10

14 1/4 rounds to 14

= 3 (10) x 3 (14)

D) is incorrect because you have to multiply each number by 3. (Or you can multiply by 6)

It is B)

4 0
2 years ago
Determine whether the given procedure results in a binomial distribution​ (or a distribution that can be treated as​ binomial).
MArishka [77]

Answer:

B. ​No, because the trials of the experiment are not independent and the probability of success differs from trial to trial.

Step-by-step explanation:

The first criterion of a binomial distribution is a fixed number of trials.  Selecting 5 senators means the number of trials is 5, which is a fixed number.

The next criterion is that the trials must be independent.  Selecting the senators without replacement means the trials are dependent, not independent; this means that this is not a binomial distribution.

5 0
3 years ago
Other questions:
  • Allen is showing his work in simplifying –8.3 + 9.2 – 4.4 + 3.7. Identify and explain any errors in his work or in his reasoning
    9·2 answers
  • Solve for n: -4 (3n+3) = 5 (-2-6n) -2
    13·2 answers
  • 80 POINTS The director of a local ballet company needs to print the programs for the next performance. Janet’s Print Shop charge
    5·2 answers
  • (I need help ASAP)
    14·1 answer
  • Can a triangle be formed with the sides lengths of 10 cm, 2 cm and 12 cm?
    12·1 answer
  • Naomi’s parents want to have 50,000, saved for her college education, if they invest 20000 today and earn 7% interest compound a
    10·1 answer
  • Please help me on this im so overwhelmed right now
    7·2 answers
  • Please help me my eyes and brain are tired​
    9·1 answer
  • Reduce 21/24 <br> What is the answer to this?
    15·1 answer
  • Dana buys a new computer that cost $675. Sales tax is 7%. What is the total cost?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!