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
Reil [10]
3 years ago
13

Help fast, ​please

Mathematics
1 answer:
pshichka [43]3 years ago
8 0

ANSWER

1.

log_{4}(3x) = log_{4}(3) + log_{4}(x)

2.

log_{3}( \frac{27}{x} )  =  3   -   log_{3}(x)

3.

log_{4}( {x}^{5} )  = 5 log_{4}(x)

EXPLANATION

1. The given logarithmic expression is

log_{4}(3x)

Use the product rule:

log_{a}(mn)  =   log_{a}(m)  +  log_{a}(n)

We apply this rule to obtain:

log_{4}(3x) = log_{4}(3) + log_{4}(x)

2. The given logarithmic expression is

log_{3}( \frac{27}{x} )

We apply the quotient rule:

log_{a}( \frac{m}{n} )  =   log_{a}(m)   -   log_{a}(n)

This implies that;

log_{3}( \frac{27}{x} )  =   log_{3}(27)   -   log_{3}(x)

We simplify to get;

log_{3}( \frac{27}{x} )  =   log_{3}( {3}^{3} )   -   log_{3}(x)

Apply the power rule:

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

log_{3}( \frac{27}{x} )  =  3 log_{3}( {3})   -   log_{3}(x)

simplify;

log_{3}( \frac{27}{x} )  =  3 (1)  -   log_{3}(x)

log_{3}( \frac{27}{x} )  =  3   -   log_{3}(x)

3. The given logarithmic expression is;

log_{4}( {x}^{5} )

Apply the power rule of logarithms.

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

This implies that,

log_{4}( {x}^{5} )  = 5 log_{4}(x) .

You might be interested in
if one face of a cube has an area of 6.75 square inches , what is the surface area of the entire cube ?​
Travka [436]

Answer:

40.5

Step-by-step explanation:

a cube has 6 faces so 6.75 x 6 = 40.5

3 0
3 years ago
Which problem solving strategy would be best to solve this problem?
g100num [7]

Answer:

A.

Step-by-step explanation:

You should be tracking your work so that you can find a pattern within the graph to correctly write the next answer.

5 0
3 years ago
The graph shows the plans for a fence that Macy is building around her vegetable garden. Each unit on the graph represents 5 fee
ipn [44]

Answer:

70

Step-by-step explanation:

5*4=70

3 0
2 years ago
Please help asap 20 pts
makkiz [27]

Answer:

B

Step-by-step explanation:

For it to be parallel, the lines must have the same slope. So A and C are out. Basic math reveals that if you plug in (1, 8) for <em>(x, y)</em> you find B to be true.

3 0
3 years ago
If there are 70 dogs to every 5 cats how many dogs are there to 70 cats
bixtya [17]

Answer:

980

Step-by-step explanation:

they are 14 5s in 70 so you only need to multiply 14×70 =980 or you can add 70 to itself 14 times

7 0
3 years ago
Other questions:
  • Need help Urgently, Easy question<br><br> Find x.
    7·2 answers
  • In physics, it is important to use mathematical approximations. for instance, in a small angle approximation, tanα ∼ sin α . fin
    15·1 answer
  • The temperature at noon is 0°C. The temperature changes buy-3/2°C every hour for 4 hours. Write a expression to represent this s
    6·1 answer
  • 63, 70, 68, 73, 58, 67 <br> I need the mean absolute deviation for this one too.
    15·2 answers
  • Consider kite ABCD.
    10·2 answers
  • Read The Question On The PNG
    14·2 answers
  • 10x10x10x10x10 as an exponent?<br><br> Help ASAP!!!
    10·2 answers
  • Question attached,
    8·1 answer
  • HELP ME ITS DUE IN 5 MINUTES, GIVING BRAINLEST
    13·1 answer
  • The Fernandez family has a square driveway with an area of 210.25 m2. Find the perimeter of the driveway. Round your answer to t
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!