Home
Class 12
MATHS
Prove that 2/5 lt log(10) 3 lt 1/2....

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

Text Solution

AI Generated Solution

To prove that \( \frac{2}{5} < \log_{10} 3 < \frac{1}{2} \), we will break the proof into two parts: 1. Proving \( \log_{10} 3 > \frac{2}{5} \) 2. Proving \( \log_{10} 3 < \frac{1}{2} \) ### Step 1: Prove \( \log_{10} 3 > \frac{2}{5} \) Given: ...
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise ILLUSTRATION 1.9|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise ILLUSTRATION 1.10|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise ILLUSTRATION 1.7|1 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE ENGLISH|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

|log_(3) x| lt 2

Prove that 1/28 lt (28) ^(1//3)-3lt 1/27

Prove that log_(10) 2" lies between " 1/4 and 1/3 .

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

Prove that : (log_(2)10)(log_(2)80)-(log_(2)5)(log_(2)160)=4 .

Solve log_(2)|x| lt 3

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

Prove that 4 lt= int_1^3 sqrt(3+x^2) dx lt= 4sqrt(3)

Prove that pi/6 lt int_0^1(dx) (sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))

For x in (0,(pi)/(2)) prove that "sin"^(2) x lt x^(2) lt " tan"^(2) x

CENGAGE ENGLISH-LOGARITHM AND ITS PROPERTIES-ILLUSTRATION 1.8
  1. Prove that 2/5 lt log(10) 3 lt 1/2.

    Text Solution

    |