General Questions
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5a = 3125 
5a = 55
a = 5.
5(a - 3) = 5(5 - 3) = 52 = 25.
(256)0.16 x (256)0.09 = (256)(0.16 + 0.09)
= (256)0.25
= (256)(25/100)
= (256)(1/4)
= (44)(1/4)
= 44(1/4)
= 41
= 4
3x - y = 27 = 33 x - y = 3 ....(i)
3x + y = 243 = 35 x + y = 5 ....(ii)
On solving (i) and (ii), we get x = 4.
| (10)150 ÷ (10)146 = | 10150 |
| 10146 |
= 10150 - 146
= 104
= 10000.
Let (25)7.5 x (5)2.5 ÷ (125)1.5 = 5x.
| Then, | (52)7.5 x (5)2.5 | = 5x |
| (53)1.5 |
| 5(2 x 7.5) x 52.5 | = 5x |
| 5(3 x 1.5) |
| 515 x 52.5 | = 5x |
| 54.5 |
5x = 5(15 + 2.5 - 4.5)
5x = 513
x = 13.
| 1 | + | 1 | + | 1 | = ? |
| 1 + x(b - a) + x(c - a) | 1 + x(a - b) + x(c - b) | 1 + x(b - c) + x(a - c) |
| (0.04)-1.5 = |  | 4 |  | -1.5 |
| 100 |
| = | | 1 | | -(3/2) |
| 25 |
= (25)(3/2)
= (52)(3/2)
= (5)2 x (3/2)
= 53
= 125.
xz = y2 10(0.48z) = 10(2 x 0.70) = 101.40
0.48z = 1.40
| z = | 140 | = | 35 | = 2.9 (approx.) |
| 48 | 12 |
| If | |
a | |
x - 1 | = | |
b | |
x - 3 | , then the value of x is: |
| b | a |
| Given | a | | x - 1 | = | | b | | x - 3 |
| b | a |
| | a | | x - 1 | = | | a | | -(x - 3) | = | | a | | (3 - x) |
| b | b | b |
x - 1 = 3 - x
2x = 4 x = 2. 121 = 112 , hence value of a = 11 and b = 2 can be considered.
Therefore, the value of (a – 1)b + 1 = (11 – 1) 2 + 1= 103