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
Bad White [126]
3 years ago
5

Condense the following log into a single log:

Mathematics
1 answer:
Tasya [4]3 years ago
6 0

Answer:

log_{3}(x . y^\frac{1}{3} / z^5 )

Step-by-step explanation:

Given in the question an expression

log_{3} x+\frac{1}{3}log_{3} y-5log_{3} z

To Condense this log into a single log we will use logarithm rules

<h3>1)Power rule</h3>

logb(x^y) = y ∙ logb(x)

\frac{1}3}log_{3} y = log_{3}y^\frac{1}{3}

5log_{3} z = log_{3} z^5

<h3>2)Product rule</h3>

logb(x ∙ y) = logb(x) + logb(y)

log_{3} x + log_{3}y^\frac{1}{3} = log_{3}(x . y^\frac{1}{3} )

<h3>3)qoutient rule </h3>

logb(x / y) = logb(x) - logb(y)\\log_{3}(x . y^\frac{1}{3} )- log_{3} z^5

= log_{3}(x . y^\frac{1}{3} / z^5 )

You might be interested in
How are the graphs of the functions f(x) = √16^x and g(x) =3√64^x related?
liberstina [14]

Answer:- The functions f(x) and g(x) are equivalent.


Explanation:-

Given functions:- f(x)=\sqrt{16^x} and g(x)=\sqrt[3]{64^x }

Simplify the functions by using law of exponents

(a^n)^m=a^{nm}

Thus f(x)=\sqrt{16^x}=\sqrt{(4^2)^x}=\sqrt{4^{2x}} =\sqrt{(4^x)^2}=4^x

and g(x)=\sqrt[3]{64^x}=\sqrt[3]{(4^3)^x}= \sqrt[3]{4^{3x}}= \sqrt[3]{(4^x)^3}=4^x

⇒f(x)=g(x)

Therefore ,the functions f(x) and g(x) are equivalent.

7 0
3 years ago
Read 2 more answers
C Betty rearranged the movies on her shelving unit after a few days. She placed equal numbers of movies on the bottom 3 shelves,
mixas84 [53]

There are total 53 movies on the shelving unit

Step-by-step explanation:

<u>DATA</u>

Equal movies on the bottom 3 shelves: 3x

10 movies on each of the top 2 shelves = 2*10 = 20

<u>Equation:</u>

3x + 20

<u>Question:</u>

Number of movies on the shelving unit if 11 movies are on each bottom 3 shelves: x = 11

<u>Solution:</u>

3x + 20

3(11) + 20 = 33 + 20 = 53

Therefore, there are total 53 movies on the shelving unit; 20 on the top 2 shelves and 33 on the bottom 3 shelves altogether.

Keywords: equation

Learn more about equation at

  • brainly.com/question/1284310
  • brainly.com/question/13168205

#LearnwithBrainly

5 0
3 years ago
What expressions are equivalent to 649×36?
goldfiish [28.3K]
I can't see what expressions you had posted. Maybe you didn't typed it out, but 649*36=23364
7 0
2 years ago
Solve -1 &lt; x + 1 ≤ 6
andrey2020 [161]

Answer:

-2<x≤5

Step-by-step :

-1<x+1≤6 So fisrt what every we do to one side we must do to the other. In this case it's a bit different since we are dealing with inequalities.

-1<x+1≤6 I would start off by isolating x in the middle.

-1<x+1≤6 I subtracted 1 from all three sides.

-1     -1   -1

Now your equation should look like this:

-2<x≤5  Now there is really nothing much we can do here since we were just trying to get x by its self.

Answer : -2<x≤5

7 0
2 years ago
Please answer fast, this is urgent no explanation need just list answer 1,2,3etc. thanks :)
Sav [38]

Answer:

Hi There!

Step-by-step explanation:

Your Answers Are:

<h3>1: 19.3 CM</h3><h3>2: 273 CM</h3><h3>3: about 45-65 degrees</h3><h3>4: 15 CM</h3><h3>5: 25 CM</h3><h3 /><h3 />

Its hard to work w/o a ruler or a protractor, so these might be incorrect.

If this helps, though, please give me a thanks!! ^^

- abakugosimp

5 0
3 years ago
Other questions:
  • Christina took a total of 10 quizzes over the course of 5 weeks. How many weeks of school
    12·1 answer
  • If the zeroes of the polynomial x^3-3x^2+x+1 are a-b,a,a+b find a and b
    9·1 answer
  • 5x^3 + 2 algebra 9th grade ​
    7·1 answer
  • What is the answer to 13a - 8a + 9b - 4b
    8·1 answer
  • The circumference of a motor bike wheel is 40cm how much distance does it cover in two full rotation
    11·1 answer
  • −3(y−8)=33<br><br> What is the value of y?
    8·1 answer
  • Wren wants to build a box to organize her scrapbook supplies. She has a stencil set that is 12 inches wide that needs to lay fla
    6·2 answers
  • In a fish tank there are 10 clown fish, 4 angel fish, 6 puffer fish, and 5 eels. What is the probability of scooping out a clown
    5·1 answer
  • What is the solution to the system of equations?
    10·1 answer
  • Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x +
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!