as you already know, to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".
![\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{f(x)}{y}=\log_2(x+1)\implies \stackrel{\textit{quick switcheroo}}{\underline{x}=\log_2(\underline{y}+1)}\implies 2^x=2^{\log_2({y}+1)} \\\\\\ 2^x=y+1\implies 2^x-1=\stackrel{f^{-1}(x)}{y} \\\\[-0.35em] ~\dotfill\\\\ 2^2-1=f^{-1}(2)\implies 3=f^{-1}(2)](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7BLogarithm%20Cancellation%20Rules%7D%20%5C%5C%5C%5C%20log_a%20a%5Ex%20%3D%20x%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Bwe%27ll%20use%20this%20one%7D%7D%7Ba%5E%7Blog_a%20x%7D%3Dx%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cstackrel%7Bf%28x%29%7D%7By%7D%3D%5Clog_2%28x%2B1%29%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bquick%20switcheroo%7D%7D%7B%5Cunderline%7Bx%7D%3D%5Clog_2%28%5Cunderline%7By%7D%2B1%29%7D%5Cimplies%202%5Ex%3D2%5E%7B%5Clog_2%28%7By%7D%2B1%29%7D%20%5C%5C%5C%5C%5C%5C%202%5Ex%3Dy%2B1%5Cimplies%202%5Ex-1%3D%5Cstackrel%7Bf%5E%7B-1%7D%28x%29%7D%7By%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%202%5E2-1%3Df%5E%7B-1%7D%282%29%5Cimplies%203%3Df%5E%7B-1%7D%282%29)
Answer:
The answer to your question is:
Packages of pencils = 6
Packages of erasers = 5
Step-by-step explanation:
Data
Pencils = 10/package
Erasers = 12 / package
Process
Find the least common factor of 10 and 12
10 12 2
5 6 2
5 3 3
5 1 5
1
LCF = 2 x 2 x 3 x 5 = 60
Finally divide 60 by the number of pencils or erasers in each package
Packages of pencils = 60/10 = 6
Packages of erasers = 60/12 = 5
16 students is the correct answer...
for every 5 boys there are 3 girls, so 20 boys 6 girls = the total of 16 students
Answer would be 120 servings because 1 3/5 times 10 is 16, so I need to multiply 10 with 12 which is 20 the answer.
