The number can be used to get rid of all fractions is 12
<h3>What number can be used to get rid of all fractions?</h3>
The equation is given as:
6 - 3/4x + 1/3 = 1/2x + 5
The denominator of the fractions are:
4, 3 and 2
The LCM of 4, 3 and 2 is 12
So, we have:
12 * [6 - 3/4x + 1/3] = 12 * [1/2x + 5]
Evaluate the products
72 - 9x + 12 = 6x + 60
Hence, the number can be used to get rid of all fractions is 12
Read more about fractions at:
brainly.com/question/11562149
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A counterclockwise rotation of 180 degrees
Answer:
The condensed log equation is: ![\log{\frac{x^4y}{z^5}}](https://tex.z-dn.net/?f=%5Clog%7B%5Cfrac%7Bx%5E4y%7D%7Bz%5E5%7D%7D)
Step-by-step explanation:
We use these following logarithm properties to solve this question:
![a\log{x} = \log{x^a}](https://tex.z-dn.net/?f=a%5Clog%7Bx%7D%20%3D%20%5Clog%7Bx%5Ea%7D)
![\log{a} + \log{b} = \log{ab}](https://tex.z-dn.net/?f=%5Clog%7Ba%7D%20%2B%20%5Clog%7Bb%7D%20%3D%20%5Clog%7Bab%7D)
![\log{a} - \log{b} = \log{\frac{a}{b}}](https://tex.z-dn.net/?f=%5Clog%7Ba%7D%20-%20%5Clog%7Bb%7D%20%3D%20%5Clog%7B%5Cfrac%7Ba%7D%7Bb%7D%7D)
In this question:
![4\log{x} = \log{x^4}](https://tex.z-dn.net/?f=4%5Clog%7Bx%7D%20%3D%20%5Clog%7Bx%5E4%7D)
![5\log{5} = \log{z^5}](https://tex.z-dn.net/?f=5%5Clog%7B5%7D%20%3D%20%5Clog%7Bz%5E5%7D)
So
![4\log{x} + \log{y} - 5\log{z}](https://tex.z-dn.net/?f=4%5Clog%7Bx%7D%20%2B%20%5Clog%7By%7D%20-%205%5Clog%7Bz%7D)
Becomes:
![\log{x^4} + \log{y} - \log{z^5}](https://tex.z-dn.net/?f=%5Clog%7Bx%5E4%7D%20%2B%20%5Clog%7By%7D%20-%20%5Clog%7Bz%5E5%7D)
Now applying the addition and subtraction properties, we have:
![\log{\frac{x^4y}{z^5}}](https://tex.z-dn.net/?f=%5Clog%7B%5Cfrac%7Bx%5E4y%7D%7Bz%5E5%7D%7D)
The condensed log equation is: ![\log{\frac{x^4y}{z^5}}](https://tex.z-dn.net/?f=%5Clog%7B%5Cfrac%7Bx%5E4y%7D%7Bz%5E5%7D%7D)