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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We have been given that ∠Q is an acute angle such that
. We are asked to find the measure of angle Q to nearest tenth of a degree.
We will use arctan to solve for measure of angle Q as:
![Q=\text{tan}^{-1}(0.04)](https://tex.z-dn.net/?f=Q%3D%5Ctext%7Btan%7D%5E%7B-1%7D%280.04%29)
Now we will use calculator to solve for Q as:
![Q=2.290610042639^{\circ}](https://tex.z-dn.net/?f=Q%3D2.290610042639%5E%7B%5Ccirc%7D)
Upon rounding to nearest tenth of degree, we will get:
![Q=2.3^{\circ}](https://tex.z-dn.net/?f=Q%3D2.3%5E%7B%5Ccirc%7D)
Therefore, measure of angle Q is approximately 2.3 degrees.
Answer:
true
Step-by-step explanation:
4+3+9=3+4+9
use the commutative property to rearrange the terms.
4+3+9=4+3+9
equality is true because both members are identical.
Answer:
The length of the parking lot should be increased by 20 feet.
Step-by-step explanation:
First, you find the product of 120 and 80, you get 9600.
Next, add 4400 to it. You get 1400
Finally what would you add to both 120 and 80 to get 14000? 20 to get 140*100.