Home
Class 12
MATHS
Prove that 1/3 lt log(20) 3 lt 1/2....

Prove that ` 1/3 lt log_(20) 3 lt 1/2`.

Text Solution

Verified by Experts

`x= log_(20) 3`
` rArr 1/x = log_(3) 20`
We know that ` 3^(2) lt 20 lt 3^(3)`
` rArr 2 lt log_(3) 20 lt 3`
` rArr 2 lt 1/x lt 3`
` rArr x in (1/3,1/2)`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.4|12 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.5|13 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

Prove that 2/5 lt log_(10) 3 lt 1/2 .

log_(2)|x| lt 3

|log_(3) x| lt 2

Solve 1 lt log_(2)(x-2) le 2 .

Solve log_(2)|x-1| lt 1 .

Prove that sin 1^circ lt sin 1 .

Using monotonicity prove that x lt - ln (1-x) lt x (1-x)^(-1) for 0 lt x lt 1

Prove that ln 2 lt int_(0)^(1)(dx)/(sqrt(1+x^(4))) lt (pi)/2)

Prove that (x)/((1 + x)) lt log (1 + x) lt x " for " x gt 0

Statement - 1 : If x gt 1 then log_(10)x lt log_(3)x lt log_(e )x lt log_(2)x . Statement - 2 : If 0 lt x lt 1 , then log_(x)a gt log_(x)b implies a lt b .