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
8_murik_8 [283]
2 years ago
6

What is the solution to log2(2x^3-8)-2log2x=log2x?

Mathematics
1 answer:
Alexxandr [17]2 years ago
5 0

Answer:

<h2>x = 2</h2>

Step-by-step explanation:

\\\\\text{Domain:}\\\\2x^3-8>0\ \wedge\ x>0\\2x^2>8\to  x^3>4\to x>\sqrt[3]4\\\\x\in(\sqrt[3]{4},\ \infty)\\\\\log_2(2x^3-8)-2\log_2x=\log_2x\qquad\text{add}\ 2\log_2x\ \text{to both sides}\\\\\log_2(2x^3-8)=3\log_2x\qquad\text{use}\ n\log_ab=\log_ab^n\\\\\log_2(2x^3-8)=\log_2x^3\iff2x^3-8=x^3\qquad\text{subtract}\ 2x^3\ \text{from both sides}\\\\-8=-x^3\qquad\text{change the signs}\\\\8=x^3\to x=\sqrt[3]8\\\\x=2\in D

You might be interested in
Can someone help me with this please
Annette [7]

Answer:

The answer to your question is A.

6 0
2 years ago
There are eight students in a class. Only one of them has passed Exam P/1 and only one of them has passed Exam FM/2. No student
Svetach [21]

Answer: There is probability of 0.57 chances that exactly three students from a group of four students have not passed Exam P/1 or Exam FM/2.

Step-by-step explanation:

Total number of students = 8

Number of student who has passed Exam P/1 = 1

Number of student who has passed Exam FM/2 = 1

No student has passed more than one exam.

According to question, exactly three students from a randomly chose group of four students have not passed Exam P/1 or Exam FM/2.

So, Probability will be

\frac{^6C_3\times ^2C_1}{^8C_4}\\\\=\frac{20\times 2}{70}\\\\=\frac{4}{7}\\\\=0.57

Hence, there is probability of 0.57 chances that exactly three students from a group of four students have not passed Exam P/1 or Exam FM/2.

4 0
3 years ago
Almost done. I need help with this part
valentina_108 [34]

Answer:

\%Percent = 14.3\%

Step-by-step explanation:

Required

15 is what percentage of 105

To do this, simply divide 15 by 105 multiplied by 100%.

So, we have:

\%Percent = \frac{15}{105} * 100\%

\%Percent = \frac{15*100}{105}\%

\%Percent = \frac{1500}{105}\%

\%Percent = 14.3\% --- approximated

8 0
3 years ago
During a baseball game, a food stand sells popcorn for $2.50 and hotdogs for $3 each. If at the end of the game, the stand made
nasty-shy [4]
Let
x-------> bags of <span>popcorn
</span>y-------> bags of hotdogs

we know that
2.50x+3y=200-------> equation 1
x=2y--------> equation 2

substitute 2 in 1

2.50*[2y]+3y=200--------> 5y+3y=200------> 8y=200-----> y=200/8
y=25
x=2y-----> x=2*25-----> x=50

the answer is
50 bags of popcorn
25 bags of hotdogs<span />
5 0
3 years ago
Which shows the prime factorization of 80? Check all that apply. 2 × 4 × 10 2 × 2 × 2 × 2 × 5 24 × 5 2 × 5 × 8
TEA [102]

Answer:

The Prime Factorization of 80 is,  2 × 4 × 10, 2 × 2 × 2 × 2 × 5  and  2 × 4 × 10

Step-by-step explanation: They are correct, because they all equal 80. 2 × 4 × 10=80 and  2 × 4 × 10=80, and 2 × 2 × 2 × 2 × 5=80.

24 × 5=120, Therefore it's the only incorrect question.

4 0
3 years ago
Read 2 more answers
Other questions:
  • Write a recursive definition for the sequence 14, 10, 6, 2,… Common difference is 4 what do I do next?
    14·2 answers
  • The measure of an angle is 51°. What is the measure of its complement? A. 39° B. 49° C. 129° D. 139°
    15·1 answer
  • The night watchman in a factory cannot guard both the safe in back and the cash register in front. The safe contains $6000, whil
    12·1 answer
  • An equation is shown below: (ALSO GET 35 POINTS!!!)
    12·1 answer
  • -9 is less than w and w is less than or equal to -3
    15·1 answer
  • Consider the perimeter of a rectangle being 68 cm and the width being 4 less than the length. Write a linear relation in terms o
    8·1 answer
  • Pls help ................
    10·2 answers
  • WILL GIVE BRAINLIEST!!!<br> What is your favorite color?
    15·1 answer
  • Please give me the correct answer.Only answer if you're very good at math.Please don't use a link to a website.​
    5·2 answers
  • Can anyone help me? =)
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!