Home
Class 12
MATHS
Solve (0.5)^(log(3)log((1//5)))(x^(2)-4/...

Solve `(0.5)^(log_(3)log_((1//5)))(x^(2)-4/5)gt 1`.

Text Solution

Verified by Experts

The correct Answer is:
`x in(-3/sqrt5, - 1)cup(1, 3/sqrt5)`
`(0.5)^(log_(3) log_((1//5))(x^(2)-4/5)) gt 1`
`rArr (1/2)^(log_(3)log_(1//5)(x^(2)-4/5))gt(1/2)^(0)`
` rArr log_(3) log_(1//5)(x^(2)-4/5)lt0`
` rArr 0 lt log_(1//5)(x^(2)-4/5) lt 1`
` rArr 1 gt x^(2) - 4/5 gt 1/5`
` rArr 1 lt x^(2) lt9/5`
` rArr x in(-3/sqrt5,-1)uu(1,3/sqrt5)`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise Exercise 1.6|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise Exercises (Single Correct Answer Type)|50 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise Exercise 1.4|12 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

Solve log_(1//3)(x^(2)-3x+5)lt -1

(0. 5)^((log_(1/3) ((x+5)/(x^2+3)))>1

Solve log_(3)|x|gt 2 .

The domain of definition of the function f(x) = log_(3) {-log_(1//2)(1+(1)/(x^(1//5)))-1}

Solve log_(3)(x+2)(x+4)+log_(1//3)(x+2) lt 1/2 log_(sqrt3)7 .

Solve for x: a) log_(0.5)(x^(2)-5x+6) ge -1 , b) log_(1//3)(log_(4)(x^(2)-5)) gt 0

Solve log_((1)/(3))(x-1)>log_((1)/(3))4 .

Solve the equation: 2log_(3)x+log_(3)(x^(2)-3)=log_(3)0.5+5^(log_(5)(log_(3)8)

Solve 2^(log_(2)(x-1))gtx+5 .

Solve: log_(0.1)(x^(2)+x-2)>log_(0.1)(x+3)