General Questions
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4 (x – y) = 64
4 (x – y) = 64 = 43
Equation 1) x – y = 3
4 (x + y) = 1024 = 45
Equation 2) x + y = 5
Solving equation (1) and (2), we get
x = 4 and y = 1
Crosscheck the answers by substituting the values of x and y in the given expression.
4 (4 – 1) = 43 = 64 and 4 (4 + 1) = 45 = 1024
Hence, the answers x = 4 and y = 1 are correct.
xm × xn = xm + n
9x – 9x – 1 = 648
9x – 1 (9 – 1) = 648
9x – 1 = (648/8) = 81
9x – 1 = 92
x – 1 = 2
x = 2 + 1 = 3
xx = 33 = 27
Alternate solution:
Select the given options and substitute the value of x = 5, 6, 1.5 and 3 in the given expression.
Substituting value of x = 3,
9x – 9x – 1 = ?
93 – 93 – 1 = 648
Value of x = 3
xx = 33 = 27
We know that 112 = 121.
Putting m = 11 and n = 2, we get:
(m - 1)n + 1 = (11 - 1)(2 + 1) = 103 = 1000.
Let (17)3.5 x (17)x = 178.
Then, (17)3.5 + x = 178.
3.5 + x = 8
x = (8 - 3.5)
x = 4.5
| (243)n/5 x 32n + 1 | = ? |
9n x 3n - 1 |
| Given Expression |
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Cube root of 1331 is 11. Therefore,
(113)– (2/3)
Hint:
Remember the law of indices (xm)n = xmn (11) – 3 × (2/3) = 11–2
Hint: x-1 = 1/x
11-2 = 1/121