log_x2(81-24x) = 1

81 – 24x = ()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

log₂(p – 1) + 2 = log₂(3p + 1)

2 = log₂(2₂)

Thus, log₂(p – 1) + log₂(2₂) = log₂(3p + 1)

log₂((p – 1)*(2₂)) = log₂(3p + 1)

(p - 1)(2₂) = 3p + 1

4p – 4 = 3p + 1

4p – 3p = 1 + 4

p = 5