Answer:
6
Step-by-step explanation:
When you do 3×6 you get 18 and when you do 5×6 you get 30
Answer:
3(x+6)
Step-by-step explanation:
Parenthesis after a number typically means multiply, so 3 times the sum of an unspecified number (x), plus 6 would be 3 (x+6)
Answer:
![x = 16](https://tex.z-dn.net/?f=x%20%3D%2016)
Step-by-step explanation:
Given
![log_{16}(x) + log_4(x) + log_2(x) = 7](https://tex.z-dn.net/?f=log_%7B16%7D%28x%29%20%2B%20log_4%28x%29%20%2B%20log_2%28x%29%20%3D%207)
Required
Solve for x
![log_{16}(x) + log_4(x) + log_2(x) = 7](https://tex.z-dn.net/?f=log_%7B16%7D%28x%29%20%2B%20log_4%28x%29%20%2B%20log_2%28x%29%20%3D%207)
Change base of 16 and base of 4 to base 2
![\frac{log_2(x)}{log_2(16)} + \frac{log_2(x)}{log_2(4)} + log_2(x) = 7](https://tex.z-dn.net/?f=%5Cfrac%7Blog_2%28x%29%7D%7Blog_2%2816%29%7D%20%2B%20%5Cfrac%7Blog_2%28x%29%7D%7Blog_2%284%29%7D%20%2B%20log_2%28x%29%20%3D%207)
Express 16 and 4 as 2^4 and 2^2 respectively
![\frac{log_2(x)}{log_2(2^4)} + \frac{log_2(x)}{log_2(2^2)} + log_2(x) = 7](https://tex.z-dn.net/?f=%5Cfrac%7Blog_2%28x%29%7D%7Blog_2%282%5E4%29%7D%20%2B%20%5Cfrac%7Blog_2%28x%29%7D%7Blog_2%282%5E2%29%7D%20%2B%20log_2%28x%29%20%3D%207)
The above can be rewritten as:
![\frac{log_2(x)}{4log_22} + \frac{log_2(x)}{2log_22} + log_2(x) = 7](https://tex.z-dn.net/?f=%5Cfrac%7Blog_2%28x%29%7D%7B4log_22%7D%20%2B%20%5Cfrac%7Blog_2%28x%29%7D%7B2log_22%7D%20%2B%20log_2%28x%29%20%3D%207)
![log_22 = 1](https://tex.z-dn.net/?f=log_22%20%3D%201)
So, we have:
![\frac{log_2(x)}{4*1} + \frac{log_2(x)}{2*1} + log_2(x) = 7](https://tex.z-dn.net/?f=%5Cfrac%7Blog_2%28x%29%7D%7B4%2A1%7D%20%2B%20%5Cfrac%7Blog_2%28x%29%7D%7B2%2A1%7D%20%2B%20log_2%28x%29%20%3D%207)
![\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x) = 7](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7Dlog_2%28x%29%20%2B%20%5Cfrac%7B1%7D%7B2%7Dlog_2%28x%29%20%2B%20log_2%28x%29%20%3D%207)
Multiply through by 4
![4(\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x)) = 7 * 4](https://tex.z-dn.net/?f=4%28%5Cfrac%7B1%7D%7B4%7Dlog_2%28x%29%20%2B%20%5Cfrac%7B1%7D%7B2%7Dlog_2%28x%29%20%2B%20log_2%28x%29%29%20%3D%207%20%2A%204)
![log_2(x) + 2}log_2(x) + 4log_2(x) = 28](https://tex.z-dn.net/?f=log_2%28x%29%20%2B%202%7Dlog_2%28x%29%20%2B%204log_2%28x%29%20%3D%2028)
![7log_2(x) = 28](https://tex.z-dn.net/?f=7log_2%28x%29%20%3D%2028)
Divide through by 7
![\frac{7log_2(x)}{7} = \frac{28}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B7log_2%28x%29%7D%7B7%7D%20%3D%20%5Cfrac%7B28%7D%7B7%7D)
![log_2(x) = 4](https://tex.z-dn.net/?f=log_2%28x%29%20%3D%204)
Apply the following law of logarithm:
<em>If </em>
<em> </em><em>Then </em>
<em></em>
So, we have:
![x = 2^4](https://tex.z-dn.net/?f=x%20%3D%202%5E4)
![x = 16](https://tex.z-dn.net/?f=x%20%3D%2016)
Answer:
![\frac{9}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B5%7D)
Step-by-step explanation:
the slope is the change in y over the change in x
From the points given, your y's are 10 and 1.
From the points given, your x's are 7 and 2. To find the changes subtract them.
= ![\frac{9}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B5%7D)