Home
Class 12
MATHS
Prove that number log(2) 7 is an irrati...

Prove that number ` log_(2)` 7 is an irrational number.

Text Solution

Verified by Experts

Let ` log_(2) 7 ` is a rational number. Then,
` log_(2)7=p/q , p,q in Q or 7 = 2^(p//q) or 7^(q) = 2^(p)`
which is not possible for any integral values of p and q.
Hence, ` log_(2) 7 ` is not rational.
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.1|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.2|9 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

The number log_(2) 7 is

Show that the number log _(2)(7) is an irrational number

Show that log_(2)(7) is an irrational number.

The number log_2 7 is :

Prove sqrt(2) is an irrational number.

The number log _(2)(7) is

Show that log_(4)18 is an irrational number.

Prove sqrt(6) is an irrational number.