The correct answr is 24 3/4 just took the test
Answer:
![\log_{81}(27)=\frac{3}{4}](https://tex.z-dn.net/?f=%5Clog_%7B81%7D%2827%29%3D%5Cfrac%7B3%7D%7B4%7D)
Step-by-step explanation:
The given logarithm is
![\log_{81}(27)](https://tex.z-dn.net/?f=%5Clog_%7B81%7D%2827%29)
Let us change to base 3.
![\log_{81}(27)=\frac{\log_3(27)}{\log_3(81)}](https://tex.z-dn.net/?f=%5Clog_%7B81%7D%2827%29%3D%5Cfrac%7B%5Clog_3%2827%29%7D%7B%5Clog_3%2881%29%7D)
![\log_{81}(27)=\frac{\log_3(3^3)}{\log_3(3^4)}](https://tex.z-dn.net/?f=%5Clog_%7B81%7D%2827%29%3D%5Cfrac%7B%5Clog_3%283%5E3%29%7D%7B%5Clog_3%283%5E4%29%7D)
![\log_{81}(27)=\frac{3\log_3(3)}{4\log_3(3)}](https://tex.z-dn.net/?f=%5Clog_%7B81%7D%2827%29%3D%5Cfrac%7B3%5Clog_3%283%29%7D%7B4%5Clog_3%283%29%7D)
![\log_{81}(27)=\frac{3(1)}{4(1)}](https://tex.z-dn.net/?f=%5Clog_%7B81%7D%2827%29%3D%5Cfrac%7B3%281%29%7D%7B4%281%29%7D)
![\log_{81}(27)=\frac{3}{4}](https://tex.z-dn.net/?f=%5Clog_%7B81%7D%2827%29%3D%5Cfrac%7B3%7D%7B4%7D)
There are 15 mini hotdogs and 5 mini pizza rolls in the combination meal.
Step-by-step explanation:
Given,
Calories in each hotdog = 80 calories
Calories in each mini pizza = 50 calories
Combined meal = 20
Combined calories = 1450 calories
Let,
x represent the number of hot dogs.
y represent the number of mini pizzas.
According to given statement;
x+y=20 Eqn 1
80x+50y=1450 Eqn 2
Multiplying Eqn 1 by 80
![80(x+y=20)\\80x+80y=1600\ \ \ Eqn\ 3](https://tex.z-dn.net/?f=80%28x%2By%3D20%29%5C%5C80x%2B80y%3D1600%5C%20%5C%20%5C%20Eqn%5C%203)
Subtracting Eqn 2 from Eqn 3
![(80x+80y)-(80x+50y)=1600-1450\\80x+80y-80x-50y=150\\30y=150](https://tex.z-dn.net/?f=%2880x%2B80y%29-%2880x%2B50y%29%3D1600-1450%5C%5C80x%2B80y-80x-50y%3D150%5C%5C30y%3D150)
Dividing both sides by 30
![\frac{30y}{30}=\frac{150}{30}\\y=5](https://tex.z-dn.net/?f=%5Cfrac%7B30y%7D%7B30%7D%3D%5Cfrac%7B150%7D%7B30%7D%5C%5Cy%3D5)
Putting y=5 in Eqn 1
![x+5=20\\x=20-5\\x=15](https://tex.z-dn.net/?f=x%2B5%3D20%5C%5Cx%3D20-5%5C%5Cx%3D15)
There are 15 mini hotdogs and 5 mini pizza rolls in the combination meal.
Keywords: linear equation, elimination method
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