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
More Quant Miscellaneous Questions
- Select the number from among the given options that can replace the question mark (?) in the following series.
17, 18, 22, 31, 47, ___ - Which letter-cluster will replace the question mark (?) in the following series?
NPQR, OORQ, PNSP, ____, RLUN - A series is given with one term missing. Choose the correct alternatives from the given ones that will complete the series.
57, 59, 56, 61, 54, ___ - Which letter and number cluster will replace the question mark (?) to complete the given series?
LT6, KU12, IW24, FZ48, ____ - Which letter-cluster will replace the question mark (?) in the following series?
RGV, UME, ?, AYW, DEF
