Question
If log₂(x) + log₄(x) + log₈(x) = 11, with x > 0,
then the value of x is:Solution
ATQ, We convert all logarithms to the same base (base 2). Note that: 4 = 2², so log₄(x) = log₂(x) / log₂(4) = log₂(x) / 2 8 = 2³, so log₈(x) = log₂(x) / log₂(8) = log₂(x) / 3 Let y = log₂(x). Then the equation becomes: y + (y/2) + (y/3) = 11 Find a common denominator (6): (6y/6) + (3y/6) + (2y/6) = 11 (11y/6) = 11 So: 11y/6 = 11 y = 11 * (6/11) y = 6 Recall y = log₂(x), So: log₂(x) = 6 x = 2⁶ = 64 Therefore, x = 64
What will come in place of the question mark (?) in the following series?
45, 66, 44, 67, 43, ?
10296/72 + 3040 = (? × 4) + 1395
What value should come in the place of (?) in the following number series?
71, 72, 76, 103, ?, 244What will come in place of the question mark (?) in the following series?
75, ?, 107, 148, 229, 390
What will come in place of the question mark (?) in the following series?
25, 25, 5, 10, 2, ?
126 56 ? 12 10 2
...80, 120, 30, 45, 9, 13.5, ?
37, 57, 82, ?, 147, 187
135, 148, ?, 184, 207, 236
25 25 37.5 ? 328.125 1804.6875
