The logarithm written as a sum of logarithm and simplified as much as possible is ![\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%2Blog_%7B4%20%7D3%20%2B%20%20log_%7B4%20%7Da%20%2B%20log_%7B4%20%7Db)
<h3>Simplifying Logarithms</h3>
From the question, we are to write the given logarithm expression as a sum or difference of logarithms
The given logarithm is
![log_{4 }6ab](https://tex.z-dn.net/?f=log_%7B4%20%7D6ab)
This can be written as
![log_{4 }6 \times a \times b](https://tex.z-dn.net/?f=log_%7B4%20%7D6%20%5Ctimes%20a%20%5Ctimes%20b)
From one of the rules of logarithm, we have that
![log_{x }yz= log_{x }y + log_{x }z](https://tex.z-dn.net/?f=log_%7Bx%20%7Dyz%3D%20log_%7Bx%20%7Dy%20%2B%20log_%7Bx%20%7Dz)
Thus,
becomes
![log_{4 }6 + log_{4 }a + log_{4 }b](https://tex.z-dn.net/?f=log_%7B4%20%7D6%20%2B%20log_%7B4%20%7Da%20%2B%20log_%7B4%20%7Db)
This can be further simplified into
![log_{4 }3 \times 2 + log_{4 }a + log_{4 }b](https://tex.z-dn.net/?f=log_%7B4%20%7D3%20%5Ctimes%202%20%2B%20log_%7B4%20%7Da%20%2B%20log_%7B4%20%7Db)
![log_{4 }3 + log_{4 }2 + log_{4 }a + log_{4 }b](https://tex.z-dn.net/?f=log_%7B4%20%7D3%20%2B%20log_%7B4%20%7D2%20%2B%20log_%7B4%20%7Da%20%2B%20log_%7B4%20%7Db)
If desired, this can be further simplified into
![log_{4 }3 + log_{2^{2} }2 + log_{4 }a + log_{4 }b](https://tex.z-dn.net/?f=log_%7B4%20%7D3%20%2B%20log_%7B2%5E%7B2%7D%20%20%7D2%20%2B%20log_%7B4%20%7Da%20%2B%20log_%7B4%20%7Db)
![log_{4 }3 + \frac{1}{2} log_{2}2 + log_{4 }a + log_{4 }b](https://tex.z-dn.net/?f=log_%7B4%20%7D3%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20log_%7B2%7D2%20%2B%20log_%7B4%20%7Da%20%2B%20log_%7B4%20%7Db)
![log_{4 }3 + \frac{1}{2} (1)+ log_{4 }a + log_{4 }b](https://tex.z-dn.net/?f=log_%7B4%20%7D3%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%281%29%2B%20log_%7B4%20%7Da%20%2B%20log_%7B4%20%7Db)
![\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%2Blog_%7B4%20%7D3%20%2B%20%20log_%7B4%20%7Da%20%2B%20log_%7B4%20%7Db)
Hence, the logarithm written as a sum of logarithm and simplified as much as possible is ![\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%2Blog_%7B4%20%7D3%20%2B%20%20log_%7B4%20%7Da%20%2B%20log_%7B4%20%7Db)
Learn more on Simplifying logarithms here: brainly.com/question/17851187
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Answer:
4pi
Step-by-step explanation:
area of a circle is pi*r^2
and you have diameter of 4
so 4/2 gives radius which is 2
A = pi*2^2 = 4pi
Answer:
-2
Step-by-step explanation:
To solve you need to replace the variables with their numbers.
3(-1) - (-1^2)
-1 x -1 = -1
3 x (-1) = -3
-3 - (-1) =
-2
Answer:
-10
Step-by-step explanation:
7 + 7(-4) - (2(-4)) + 3
7 - 28 - (-8)+3
7 - 28 +8 +3
= -10
Answer:
7 %
Step-by-step explanation:
- i do not know if you use this but I use S.I=P×R/100×T
- S.I=840
- P for principal(the money you borrow or lend) =6000
- T for time=2 years.
- R for rate=???
- In order to find out the rate, you need to substitute all these numbers into their respective places.
- 840=6000×r/100×2
- 6000/100=60
- 840=60×r×2
- 840=120r
- r=7%