Home
Class 12
MATHS
Prove that logn(n+1)>log(n+1)(n+2) for a...

Prove that `log_n(n+1)>log_(n+1)(n+2)` for any natural number `n > 1.`

Text Solution

Verified by Experts

The correct Answer is:
`because log_(n)(n+1) gt log_((n+1))(n+2)` Hence proved.
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND THEIR PROPERTIES

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos
  • LOGARITHM AND THEIR PROPERTIES

    ARIHANT MATHS|Exercise Exercise For Session 2|5 Videos
  • LIMITS

    ARIHANT MATHS|Exercise Exercise For Session 6|4 Videos
  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

prove that 1+5+9+ . . .+(4n-3)=n(2n-1), for all natural number n.

Prove that (n!+1) is not divisible by any natural number between 2 and n

Prove that 1+2+2^(2)+ . . .+2^(n)=2^(n+1)-1 , for all natural number n.

Prove that (1)/(n+1)+(1)/(n+2)+...+(1)/(2n)>(13)/(24) ,for all natural number n>1

Prove the following by using the principle of mathematical induction. n(n+1)+1 is an odd natural number, n in N .

Prove that ((log)_(a)N)/((log)_(ab)N)=1+(log)_(a)b

For natural number n , 2^n (n-1)!lt n^n , if

Prove by the principle of mathematical induction, that 1.1!+2.2!+3.3!+.....+(n.n!)=(n+1)!-1"for all natural number "n (n!=1xx2xx3....n)

The number of values of n such that log_(n) 2^(231) is an integer is (n in N)