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
yarga [219]
3 years ago
8

Use the properties of logarithms to expand the following expression.log(z3)/√x5y)Each logarithm should involve only one variable

and should not have any radicals or exponents. You may assume that all variables are positive.
Mathematics
1 answer:
jek_recluse [69]3 years ago
8 0

Answer:

3 log (z) -  1/2log (x) - 1/2 log (5) -1/2 log y

Step-by-step explanation:

log(z3)/√x5y)

= log (z3)   - log (√x5y)   [division being subtracted]

= 3 log (z) - {log (√x) + log (√5y)}    [ multiplication being added in the denominator]

= 3 log (z) - {log (x)^1/2 + log (5)^1/2+ log (y)^1/2}  

= 3 log (z) -  1/2{log (x) + log (5)+ log y }

 We can solve inside the curly bracket and then multiply with 1/2 or we can solve it separately

= 3 log (z) -  1/2log (x) - 1/2 log (5) -1/2 log y

How does this work?

1) any two terms being multiplied in logarithms are added with the log of each.

2) the exponent becomes the co- efficient.

3)  any two terms being divided in logarithms are subtracted with the log of each

You might be interested in
MARKING BRAINLIST! PLEASE HELP!
Leviafan [203]

Answer:

\boxed {\boxed {\sf C. \ 4 \ inches}}

Step-by-step explanation:

Circumference is the perimeter of a circle. It can be found using the formula:

c= \pi d

However, we are given the radius.

  • The radius measures from the center to the edge of the circle.
  • The diameter measures from edge to edge through the center.
  • So, the diameter is twice the radius, or d=2r

The formula can be rewritten as:

c= \pi 2 r

We know the circumference is 25.12 inches.

25.12 \ in = \pi 2r

Let's round pi to 3.14

25.12 \ in = (3.14) 2r

We want to solve for the radius, so we must isolate it.

Divide both sides by 3.14 because the inverse of multiplication is division.

25.12 \ in / 3.14= (3.14 ) 2r  / 3.14

8 \ in = 2r

Divide both sides by 2.

8 \ in / 2 = 2r/2

4 \ in = r

The radius of the disc is <u>4 inches.</u>

6 0
3 years ago
22. Use your model to determine when the volume of oil will get down to 500 gallons.
Helen [10]

Answer:

  21.  y = 75000·0.935^t

  22.  after 74.6 days

  23.  y = 27.8112·1.18832^t

  24.  18.8% per month

  25.  1748

Step-by-step explanation:

22. It is convenient to use the graphing calculator to solve this problem. The number of days is where the exponential curve has the value 500. It is about 74.55 days. (see the first attachment)

__

23. y = 27.8112·1.18832^t (see the second attachment)

__

24. The rate of change is the difference between the base of the exponential and 1, often expressed as a percentage. The time period is the units of t.

  (1.18832 -1) × 100% ≈ 18.8% . . . . per month

__

25. Evaluating the function for t=24 gives y ≈ 1748.30425259 ≈ 1748.

_____

<em>Comment on graphing calculator</em>

A graphing calculator can make very short work of problems like these. It is worthwhile to get to know how to use one well.

8 0
3 years ago
The width of a rectangle is 38 centimeters. the perimeter is at least 692 centimeters. write an inequality that represents all p
abruzzese [7]

Width of the reactangle = 38 cm

Minimum perimeter = 692 cm

Let the length of the rectangle be x cm

We know that,

Perimeter of rectangle = 2 * (length + width)

Since the perimeter should be atleast 692 cm. Therefore,

2 * (x + 38) > 692

2x + 76 > 692

2x > 692 - 76

2x > 616

x > \frac{616}{2}

x > 308

Hence, the length of the rectangle should be more that 308 cms.

4 0
3 years ago
Help me
Korolek [52]

Answer:

GIVE ME MY RAMEN

Step-by-step explanation:

3.

add like terms

30 + 7k = 100

100-30 = 70

70 divided by 7k = 10

k = 10

4. add the z's together

2z - 6 -2 = -10

+ 6 + 2

-10 will be -2 now since we dragged the -6 and -2 to the other side

2z = -2

z = -1

5. 3.2x - 1.7x = 1.5x

1.5x + 5.5 = 10

10 would be 4.5 since we dragged 5.5 to the other side so it would be 10 - 5.5

3.2x = 5.5

x = 1.71875

6.

3/4x - 1/4x = 2/4x

14 - 3 = 11

2/4x = 11

x = 22

7 0
3 years ago
27 minus 9X +15 Y please
Oksanka [162]

27 - 9x +15y

Factor out common  term 3 :

3(9-3x+5y)

hope this helps!

7 0
3 years ago
Read 2 more answers
Other questions:
  • PLEASE HELP!!!!!!!!​
    8·1 answer
  • The diameter of a circle is 22 inches.
    11·2 answers
  • Wich ratio is not equivalent to the other 3?
    9·2 answers
  • Tell whether the number is prime or composite 68,52,63, 75, 31, 77, 59, 87
    14·2 answers
  • What is 4²(4²)? <br> 2. 5⁴(5)÷2¹? <br> 3. (5+3)²? <br> Solve the following expressions
    5·1 answer
  • Examine the geometric relationships in the diagram below which option shows the correct value of x and y?
    12·1 answer
  • Square root of -1 = 1. Math test
    11·1 answer
  • Chemistry: hydroluronic acid formula
    8·1 answer
  • What is the probability you would spin a yellow or green space on this spinner?
    7·2 answers
  • Solve the system of equations using the substitution method.y=2,2x+y=8
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!