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
kakasveta [241]
3 years ago
5

Condense the following logs into a single log:

Mathematics
1 answer:
mamaluj [8]3 years ago
7 0

QUESTION 1

The given logarithm is

8\log_g(x)+5\log_g(y)

We apply the power rule of logarithms; n\log_a(m)=\log_(m^n)

=\log_g(x^8)+\log_g(y^5)

We now apply the product rule of logarithm;

\log_a(m)+\log_a(n)=\log_a(mn)

=\log_g(x^8y^5)

QUESTION 2

The given logarithm is

8\log_5(x)+\frac{3}{4}\log_5(y)-5\log_5(z)

We apply the power rule of logarithm to get;

=\log_5(x^8)+\log_5(y^{\frac{3}{4}})-\log_5(z^5)

We apply the product to obtain;

=\log_5(x^8\times y^{\frac{3}{4}})-\log_5(z^5)

We apply the quotient rule; \log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )

=\log_5(\frac{x^8\times y^{\frac{3}{4}}}{z^5})

=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})

You might be interested in
This figure shows △XYZ . MZ¯¯¯¯¯¯ is the angle bisector of ∠YZX . What is XM ? Enter your answer, as a decimal, in the box. unit
astraxan [27]

Answer:

Length of XM is 5.5 units.

Step-by-step explanation:

Given △XYZ where MZ is the angle bisector of ∠YZX . we have to find the length of XM.

A triangle with vertices  X, Y, and Z. Side XZ is base. A line segment drawn from Z to M bisects ∠YZX into two parts ∠YZM and ∠XZM.

YZ=7 units, XZ=11 units and YM=3.5 units

By angle bisector theorem which states that an angle bisector of an angle divides the opposite side in two segments that are proportional to the another two sides of the triangle.

Hence, \frac{YM}{MX}=\frac{YZ}{XZ}

⇒ \frac{3.5}{MX}=\frac{7}{11}

⇒ MX=5.5 units.

Hence, length of XM is 5.5 units.


4 0
3 years ago
Read 2 more answers
The table below shows the ticket rates for whale watching trips offered by Ocean Tours. Age Ticket Price Under three years free
Mamont248 [21]
If there are 40 children aged twelve and under and x of them are under three years old, 40 - x aged three twelve years old. From the 92 people that where taken by the company on whale watching trips, 52 are over twelve years old. The equation that best show the total cost, C is
                                (40 - x)(36) + (52)(48) = C
Rearranging the equation gives,
                                       x = 40 - ((C - 2496)/ 36)
4 0
3 years ago
Riley brought cupcakes to a party. by the end of the party 5/6 of the cupcakes were gone. what fraction of the cupcakes were lef
lions [1.4K]

Answer:

1/6

Step-by-step explanation:

this seems too simple but...

6/6 would be all the cupcakes the whole

so if 5/6 are gone than

1/6 are left

8 0
2 years ago
Read 2 more answers
Find the circumference of a circle with each 18.2cm diameter​
e-lub [12.9K]

Answer:

22/7×18.2

=400.4/7

=57.2cm

6 0
3 years ago
Ms. Lynch has 21 coins in nickels and dimes. Their total value is $1. 65. How many of each coin does she have? Please answer!!
timama [110]

Hi, there

<u>Question:Ms. Lynch has 21 coins in nickels and dimes. Their total value is $1. 65. How many of each coin does she have?</u>

Explanation:

1.65 x 21

Answer 34.65

3 0
3 years ago
Read 2 more answers
Other questions:
  • Write the standard form of an equation with p=12, phi=pi/4
    12·2 answers
  • This week, we are covering relationships that can be approximated by linear equations. For instance, y = 453x + 3768 represents
    10·1 answer
  • According to the pay stub, how much did this employee pay in FICA tax for this pay period? A) $648.51 B) $864.15 C) $215.64 D) $
    5·2 answers
  • Which form must be filled out and submitted to determine the types and amount of financial aid available to a student?
    9·2 answers
  • One machines value changed by -$6400 over 5 years. THe company charges off such changes in value as depreciation. Each year an e
    8·1 answer
  • Could someone explain how to solve problems like these? and give the answers?
    8·1 answer
  • Each morning papa notes the birds feeding on his birdfeeder. So far this month he has seen 59 blue jays, 68 black crows, 12 red
    7·2 answers
  • Explain how to find 45% of a number
    12·1 answer
  • Write an expression using only a whole number base
    7·1 answer
  • What are the characteristics of the graph of the inequality x&gt;-2
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!