Home
Class 12
MATHS
Solve 2(25)^(x) - 5 (10^(x))+2(4^(x)) g...

Solve ` 2(25)^(x) - 5 (10^(x))+2(4^(x)) ge 0`.

Text Solution

Verified by Experts

`2(25)^(x) - 5(10^(x))+2(4^(x))ge 0`
` rArr 2(5)^(2x) - 5 (5)^(x)(2^(x))+2(2^(2x))ge0`
` rArr 2(5/2)^(2x) -5 (5/2)^(x) + 2 ge 0`
` rArr [(5/2)^(x)-2][2(5/2)^(x)-1]ge0`
` rArr (5/2)^(x) le 1/2 or (5/2)^(x) ge 2`
` rArr x le log_(2.5) 0.5 or x ge log_(2.5) 2`
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

Solve :2(25)^(x)-5(10^(x))+2(4^(x))>=0

Solve 2(25)^(x)-5(10^(x))+2(4^(x))>=0

Solve : (2)/(x+3) ge 0

Solve : 2(5x - 7) ge 3(4x - 5)

Sovle x(x+2)^2(x-1)^5 (2x-3)(x-3)^4 ge 0

Solve : (x)/(6)ge (8-3x)/(2) +4

solve : (3x - 4) /(2) +1 ge (x+1)/(4)

Solve : |x| - |x-2| ge 1

Solve : 3((3x)/(5) + 4) ge 2(x-6)

Solve 2(x-3) + 4 ge 4 - x