TheCATExam
Sign in

CAT 2003 Slot 2 — QA Question 43

LogarithmsEasy
Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

  1. The first letter is any vowel.
  2. The second letter is m, n or p.
  3. If the second letter is m, then the third letter is any vowel which is different from the first letter.
  4. If the second letter is n, then the third letter is e or u.
    1. If the second letter is p, then the third letter is the same as the first letter.

If log10 x - log10 x = 2 logx 10, then a possible value of x is given by:

Answer & solution

  • A

    10

  • 1100

  • C

    11000

  • D

    None of these

Solution

log10 x - log10 x = 2 logx 10 ....(i)

Consider L.H.S of (i):

log10 x - 12 log10 x = 12 log10 x

Equating the L.H.S. and the R.H.S., we get,

log10 x = 4 logx 10

∴ log10 x = 4 logx 104

Now, let log10 x = logx 104 = y

∴ 10y = x and xy = 104

Solving these two equations, we get,

y = ±2

∴ x = 102 or x = 10–2

As x = 100 is not in the options,

∴ x = 10−2 = 1/100

Hence, option (b).

CAT 2003 Slot 2 QA Q43: If log 10 x - log 10 x = 2 log x 10, then a possible value of x is given by: — Solution | TheCATExam