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
Genrish500 [490]
3 years ago
5

3

Mathematics
1 answer:
Marianna [84]3 years ago
6 0

The expression into a single logarithm is log[(x)^{10}][(2)^{30}]

Step-by-step explanation:

Let us revise some logarithmic rules

  • log(a)^{n}=nlog(a)
  • log(ab)=log(a)+log(b)
  • nlog(a)+mlog(b)=log[(a)^{n}][(b)^{m}]

∵ 10 log(x) + 5 log(64)

- At first re-write 10 log(x)

∴  10 log(x) = log(x)^{10}

- Then re-write 5 log(64)

∴  5 log(64) = log(64)^{5}

∴ 10 log(x) + 5 log(64) = log(x)^{10} + log(64)^{5}

- Use the 3rd rule above to make it single logarithm

∵ log(x)^{10} + log(64)^{5} = log[(x)^{10}][(64)^{5}]

∴ 10 log(x) + 5 log(64) = log[(x)^{10}][(64)^{5}]

∵ 64 = 2 × 2 × 2 × 2 × 2 × 2

∴ We can write 64 as 2^{6}

∴ (64)^{5}=(2^{6})^{5}

- Multiply the two powers of 2

∴ (64)^{5}=(2)^{30}

∴ 10 log(x) + 5 log(64) = log[(x)^{10}][(2)^{30}]

The expression into a single logarithm is log[(x)^{10}][(2)^{30}]

Learn more:

You can learn more about the logarithmic functions in brainly.com/question/11921476

#LearnwithBrainly

You might be interested in
A triangle has side lengths of 7.1, 12.6, and b. Which of the following CANNOT be b? (A) 5.7 (B) 7.5 (C) 10.1 (D) 18.5 (E) 19.9
GuDViN [60]

-- When the 7.1 and 12.6 sides both point in exactly the same direction,
their open ends are 5.5 apart.  So the missing side must be greater than 5.5 . 
All of the choices are greater than 5.5 , so we haven't found it yet.

-- When the 7.1 and 12.6 point in opposite directions, their open ends are
19.7 apart.  So the missing side can't be greater than 19.7, otherwise the
two sides we know couldn't reach between its ends.  <u>Choice 'E'</u> is greater
than 19.9, so it can't be the missing side.


8 0
3 years ago
Can someone please answer ASAP !!
Leya [2.2K]
Not for 5 points sorry
5 0
3 years ago
A passenger train and a freight train leave San Jose at 3PM, traveling in the same direction. The passenger train is going three
Liono4ka [1.6K]

Let's say that the speed of the freight train is x and the one of the passenger train is 3x.

x MPH means every hour the freight train covers x miles., which means in 3h it will have covered 3 times as much: 3x mi.

Following the same logic, 3x MPH means every hour the passenger train covers 3x miles, meaning after 3h it will have covered 3 times as much as well: 9x mi.

Now, having expressed those distances and speeds algebraically, we find the difference between the two distances covered after 3h, knowing it will be equal to 240:

9x-3x=6x\\6x=240\\x=240/6\\x=40

Knowing this, we can surely affirm that the freight train is travelling at 40MPH and the passenger train is travelling three times as fast, 120MPH.

5 0
3 years ago
Identifying a constant of variation question<br><br> R= ?
jek_recluse [69]
Pressure and Volume are inversely related as:

P= \frac{R}{V}

We can also write it as:

PV=R

R is the constant of proportionality. Using the first row of given table, we can write:

2(4.155)=R \\  \\ &#10;R=8.31

Thus, the value of R, the universal gas constant is 8.31
4 0
3 years ago
Mrs Tay had 425 cookies at first.
yKpoI14uk [10]

Answer:

425-65=360

360-65=295

Mrs Chan had at first 295 cookies

3 0
3 years ago
Read 2 more answers
Other questions:
  • CD intersects AB at point G.if AE=BE which equation must be true?
    12·1 answer
  • PLEASE EXPLAIN: h(x) = sqrt(4-x^2), find the domain and range.
    5·1 answer
  • 2- 10+ x = 6 -8 + 12<br> Please answer ASAP :)
    10·2 answers
  • Pls help me answer 10, 11, and 12 thx in advance
    13·1 answer
  • 100,000 less than five hundred 60 thousand, three hundred thirteen is ___________
    7·1 answer
  • Find The GCF of 24 and 80 and Find the LCM of 24 and 40 ​
    13·2 answers
  • Brenda recorded the amount of time it took to cook potatoes in a microwave.
    11·2 answers
  • What is equation of a line parallel to y=1/2x-3 that passes through the point(3,2)? Solve by graphing or mathematically
    8·1 answer
  • Giving 18 point plz plz help
    11·1 answer
  • A spinner has many equal sections of different colors. The probability that the spinner will not land on a
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!