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
makkiz [27]
3 years ago
10

QF Q7.) Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithmic expressions

without using a calculator if possible.

Mathematics
2 answers:
Lisa [10]3 years ago
8 0
\log _9\left(\sqrt[5]{\dfrac{a^6b}{81}}\right)=\dfrac{-2+\log _9\left(b\right)+6\log _9\left(a\right)}{5} 

\log _9\left(\sqrt[5]{\dfrac{a^6b}{81}}\right) =\ \textgreater \  \log _9\left(\left(\dfrac{a^6b}{81}\right)^{\dfrac{1}{5}}\right) 

\dfrac{1}{5}\log _9\left(\dfrac{a^6b}{81}\right) 

\log _9\left(\dfrac{a^6b}{81}\right)=\log _9\left(a^6b\right)-\log _9\left(81\right) 

\log _9\left(a^6b\right)-\log _9\left(81\right) 

\log _9\left(b\right)+\log _9\left(a^6\right)-2 

6\log _9\left(a\right) 

\dfrac{1}{5}\left(6\log _9\left(a\right)+\log _9\left(b\right)-2\right) 

\dfrac{1}{5}\log _9\left(b\right)+\dfrac{1}{5}\cdot \:6\log _9\left(a\right)+\dfrac{1}{5}\left(-2\right) 

\dfrac{1}{5}\log _9\left(b\right)+\dfrac{1}{5}\cdot \:6\log _9\dleft(a\right)-\frac{1}{5}\cdot \:2) 

\dfrac{1}{5}\log _9\left(b\right)+\dfrac{1}{5}\cdot \:6\log _9\left(a\right)-\dfrac{1}{5}\cdot \:2 

\dfrac{1}{5}\cdot \:6\log _9\left(a\right)=\dfrac{6}{5}\log _9\left(a\right) 

\dfrac{1}{5}\log _9\left(b\right)+\dfrac{6}{5}\log _9\left(a\right)-\dfrac{2}{5} 

\dfrac{\log _9\left(b\right)}{5}+\log _9\left(a\right)\dfrac{6}{5}-\frac{2}{5} 

\log _9\left(a\right)\dfrac{6}{5}\::\quad \dfrac{6\log _9\left(a\right)}{5} 

\dfrac{\log _9\left(b\right)}{5}+\dfrac{6\log _9\left(a\right)}{5}-\dfrac{2}{5} 

\dfrac{\log _9\left(b\right)}{5}+\dfrac{6\log _9\left(a\right)}{5}:\quad \dfrac{\log _9\left(b\right)+6\log _9\left(a\right)}{5} =\ \textgreater \  \dfrac{-2+\log _9\left(b\right)+6\log _9\left(a\right)}{5} 

\text{Took a while, but here it is. Hope it helps!}
Softa [21]3 years ago
5 0
Attached is the solution.
The following log properties are used:
log(x^n) = nlog(x)
log(\frac{a}{b}) = log(a) - log(b) \\  \\ log(ab) = log(a) + log(b) \\  \\ log_9 (81) = 2 \rightarrow 9^2 = 81



You might be interested in
At a real estate agency, an agent sold a house for $311,000. The commission rate is 4.6% for the real
deff fn [24]

9514 1404 393

Answer:

  • agency: $14,306
  • agent: $3,576.50

Step-by-step explanation:

The agency's commission was ...

  0.046 × $311,000 = $14,306

The agent's commission was ...

  0.25 × $14,306 = $3,576.50

__

The agency made $14,306; the agent earned $3,576.50.

4 0
2 years ago
A frustum is made by removing a small cone from a similar large cone in the diagram shown the height of a small cone is a quarte
lesantik [10]

Answer:

Volume of the frustum = ⅓πh(4R² - r²)

Step-by-step explanation:

We are to determine the volume of the frustum.

Find attached the diagram obtained from the given information.

Let height of small cone = h

height of the large cone = H

The height of a small cone is a quarter of the height of the large cone:

h = ¼×H

H = 4h

Volume of the frustum = volume of the large cone - volume of small cone

volume of the large cone = ⅓πR²H

= ⅓πR²(4h) = 4/3 ×π×R²h

volume of small cone = ⅓πr²h

Volume of the frustum = 4/3 ×π×R²h -  ⅓πr²h

Volume of the frustum = ⅓(4π×R²h - πr²h)

Volume of the frustum = ⅓πh(4R² - r²)

6 0
3 years ago
Model 3+ (-4) on the number line
Anon25 [30]

Answer:

-1

Step-by-step explanation:

If u add 3 whole numbers to a negative number 4 then it'll equal -1. Think of it like 4-3 but add the negative sign at the begining

3 0
3 years ago
Read 2 more answers
Kendra bought 4 boxes of doughnuts. There were 6 doughnuts in each box. She divided the doughnuts equally among 8 people. How ma
Akimi4 [234]
Each person received 3 doughnuts, do 6 times 4 which is 24 and divide that among 8, its 3

3 0
3 years ago
Read 2 more answers
Find two numbers with a sum of 20 and a difference of 14.
Alekssandra [29.7K]
The anwser is 17 and 3. 17+3=20, and the difference is 14!
5 0
3 years ago
Read 2 more answers
Other questions:
  • 3/2x+1/5=3/4 what is the answer
    5·1 answer
  • The circle graph shows the most important problems for the
    9·1 answer
  • For the following inequality, indicate whether the boundary line should be dashed or solid.
    15·2 answers
  • U
    13·1 answer
  • Please help me thank you
    5·1 answer
  • Henry and 28 classmates go on a
    13·1 answer
  • A new car valued at 24,000 depreciates at 9% per year. What is the value of the car one year after purchase?
    10·1 answer
  • Tommy went to the mall and bought a shirt for $10 and a pair of pants for $30. Their was a sales tax of 7% on his purchase. How
    11·1 answer
  • HELP PLSS ILL GIVE BRAINLESS
    7·2 answers
  • Bob and joe have a class together at Kensington college. They leave the class at the same time. Bob goes to the library at 4 mil
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!