SOLUTION: Gud afternoon.please be so kind to assist me with the following: 1.solve the following equation 1.1. 6log4n+3log4n-3=log4n+2log4n 1.2. (x-15)3/2=27 1.3.log(x+10)=2 2. A su

Algebra ->  Finance -> SOLUTION: Gud afternoon.please be so kind to assist me with the following: 1.solve the following equation 1.1. 6log4n+3log4n-3=log4n+2log4n 1.2. (x-15)3/2=27 1.3.log(x+10)=2 2. A su      Log On


   

Question 1090141: Gud afternoon.please be so kind to assist me with the following:
1.solve the following equation
1.1. 6log4n+3log4n-3=log4n+2log4n
1.2. (x-15)3/2=27
1.3.log(x+10)=2
2. A survey carried out in a certain village that 1/2 of the people who were interviewed are youth,1/3 are people living with disability,while 1/5 of the remainder are pensioners and the remaining 2500 villagers did not take part in the survey.
2.1. show all the necessary calculation to determine the total number of people living in that village.
2.2. determine the difference in number between the people living with disability and pensioners.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1.1. 6log4n+3log4n-3=log4n+2log4n
Without brackets this problem is too ambiguous to deal with
:
1.2. (x-15)3/2=27
I think you mean
(x-15)^(3/2) = 27
Raise both sides with the exponent (2/3)
(x - 15) = 27^(2/3)
x - 15 = 9
x = 9 + 15
x = 24
;
1.3.log(x+10)=2
write this as the exponent equiv of common logs
x + 10 = 10^2
x + 10 = 100
x = 100 -10
x = 90
:
2. A survey carried out in a certain village that 1/2 of the people who were interviewed are youth,1/3 are people living with disability,while 1/5 of the remainder are pensioners and the remaining 2500 villagers did not take part in the survey.
2.1. show all the necessary calculation to determine the total number of people living in that village.
let x = total no. in the village, then
1%2F2%7D%7D%29x+=+youths%0D%0A%7B%7B%7B1%2F3x = disabled
Find the remaining, subtract the youth and disabled
x - 1%2F2x - 1%2F3x
x - 5%2F6x = 1%2F6x remain
Find 1/5 of the remaining
1%2F5*1%2F6x = 1%2F30x are pensioners
therefore
x = 1%2F2x + 1%2F3x + 1%2F30x + 2500
common denominator is 30
x = 15%2F30x + 10%2F30x + 1%2F30x + 2500
x = 26%2F30x + 2500
30%2F30x - 26%2F30x = 2500
4%2F30x = 2500
multiply both sides by 30
4x = 75000
x = 75000
x = 18750 total population of the village
:
2.2. determine the difference in number between the people living with disability and pensioners.
1%2F3(18750) = 6250 disabled
1%2F30(18750) = 625 pensioners
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the difference: = 5625