If 4\(^{3x}\) = 16\(^{x+1}\), find the value of x
2
3
4
5
Correct answer is A
4\(^{3x}\) = 4\(^{2(x+1)}\)
3x = 2x + 2
3x - 2x = 2
x = 2
2
3
5
6
Correct answer is B
23 x 54 = 1242
In mod 7;
1242 ÷ 7 = 177 R 3
Hence; 1242 ≡ 3
Given that A and B are sets such that n(A) = 8, n(B)=12 and n(AnB) =3, find n(AuB).
15
17
20
23
Correct answer is B
n(AuB) = n(A) + n(B) - n(AnB)
n(AuB) = 8 + 12 - 3
= 17
Change 432\(_{five}\) to a number in base three.
10100\(_{three}\)
11100\(_{three}\)
11101\(_{three}\)
10110\(_{three}\)
Correct answer is B
Convert from base 5 to base 10
432\(_{five}\) = (4 x 5\(^2\)) + (3 x 5\(^1\)) + (2 x 5\(^0\))
= (4 x 25) + (3 x 5) + (2 x 1)
= 100 + 15 + 2
= 117\(_{ten}\)
Then convert from base 10 to base 3
| 3 | 117 |
| 3 | 39 r 0 |
| 3 | 13 r 0 |
| 3 | 4 r 1 |
| 3 | 1 r 1 |
| 0 r 1 |
Selecting the remainders from bottom to top:
117\(_{ten}\) = 11100\(_{three}\)
Hence; 432\(_{five}\) = 11100\(_{three}\)
\(111101_{two}\)
\(11111101_{two}\)
\(1111101_{two}\)
\(11001_{two}\)
Correct answer is C
\((101_{two})^3\) = \((5_{ten})^3\)
5\(^3\) = 125
And 125 = \(1111101_{two}\)