Answer:
Option B - ![\ln(\frac{4y^5}{x^2})=\ln 4+5\ln y-2\ln x](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B4y%5E5%7D%7Bx%5E2%7D%29%3D%5Cln%204%2B5%5Cln%20y-2%5Cln%20x)
Step-by-step explanation:
Given : Expression ![\ln(\frac{4y^5}{x^2})](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B4y%5E5%7D%7Bx%5E2%7D%29)
To find : Expand each expression ?
Solution :
Using logarithmic properties,
![\ln (\frac{A}{B})=\frac{\ln A}{\ln B}=\ln A-\ln B](https://tex.z-dn.net/?f=%5Cln%20%28%5Cfrac%7BA%7D%7BB%7D%29%3D%5Cfrac%7B%5Cln%20A%7D%7B%5Cln%20B%7D%3D%5Cln%20A-%5Cln%20B)
and ![\ln (AB)=\ln A+\ln B](https://tex.z-dn.net/?f=%5Cln%20%28AB%29%3D%5Cln%20A%2B%5Cln%20B)
Here, A=4y^5 and B=x^2
![\ln(\frac{4y^5}{x^2})=\frac{\ln 4y^5}{\ln x^2}](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B4y%5E5%7D%7Bx%5E2%7D%29%3D%5Cfrac%7B%5Cln%204y%5E5%7D%7B%5Cln%20x%5E2%7D)
![\ln(\frac{4y^5}{x^2})=\ln 4y^5-\ln x^2](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B4y%5E5%7D%7Bx%5E2%7D%29%3D%5Cln%204y%5E5-%5Cln%20x%5E2)
![\ln(\frac{4y^5}{x^2})=\ln 4+\ln y^5-\ln x^2](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B4y%5E5%7D%7Bx%5E2%7D%29%3D%5Cln%204%2B%5Cln%20y%5E5-%5Cln%20x%5E2)
Using logarithmic property, ![\logx^a=a\log x](https://tex.z-dn.net/?f=%5Clogx%5Ea%3Da%5Clog%20x)
![\ln(\frac{4y^5}{x^2})=\ln 4+5\ln y-2\ln x](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B4y%5E5%7D%7Bx%5E2%7D%29%3D%5Cln%204%2B5%5Cln%20y-2%5Cln%20x)
Therefore, option B is correct.
Answer:
y= -2
Step-by-step explanation:
Please see attached picture for full solution.
(From the 4th to 5th line, I multiplied both sides by 8)
So 8w=4c and 2c=3g. divide the first equation by 2 and you get 4w=2c. merge the two equation give you 4w=2c=3g, or 4w=3g. multiply 4 on both sides give you 16w=12g. So 16 widgets equal how 12 goof-ups?
30% converted to a decimal is 0.30
310 x 0.3 = 93 students play an instrument