log_{x2}(81-24x) = 1
81 – 24x = (<sub></sub>)1
x2 + 24x -81 = 0
x2 + 27x – 3x – 81 = 0
x(x+27) – 3(x+27) = 0
(x+27)(x-3) = 0
x = 3 or – 27
Divisibility test for 8 if last 3 – digits of number is divisible by 8 then the complete number is divisible by 8.
Number = 876905 is divisible by 8 if 905 is divisible by 8.
113
8 905
- 8
10
-8
25
-24
1
As remainder is 1; 1 should be subtracted from given number to make it divisible by 8.
16 men can complete one – fourth of the work in 12 days i.e. M1 = 16, D1 = 12 and W1 = 14
M2 = ?, D2 = 12 more days i.e. 24 days and W2 = 1
Acc to chain rule: M1 x D1 x W2 = M2 x D2 x W1
16 x 12 x 1 = M2 x 24 x 14
M2 = 32 men
So, in order to complete the work in 12 more days (32 - 16) 16 more men will be needed.
Given: A = 41, B = 59, A?B?C = 98, A∩B = 15, B∩C = 20, C∩A = 25, A∩B∩C = 14
We know that;
A?B?C = A + B + C - A∩B - B∩C - C∩A + A∩B∩C
98 = 41 + 59 + C – 15 – 20 – 25 + 14
C = 44
log_{2}(p – 1) + 2 = log_{2}(3p + 1)
2 = log_{2}(2_{2})
Thus, log_{2}(p – 1) + log_{2}(2_{2}) = log_{2}(3p + 1)
log_{2}((p – 1)*(2_{2})) = log_{2}(3p + 1)
(p - 1)(2_{2}) = 3p + 1
4p – 4 = 3p + 1
4p – 3p = 1 + 4
p = 5