Home
Class 12
MATHS
Solve (3/4)^(6x+10-x^(2)) lt 27/64....

Solve` (3/4)^(6x+10-x^(2)) lt 27/64`.

Text Solution

Verified by Experts

The correct Answer is:
` -1 lt x lt 7`
`(3/4)^(6x+10-x^(2)) lt27/64`
` rArr(3/4)^(6x+10-x^(2)) lt (3/4)^(3)`
`rArr 6x + 10 - x^(2) gt 3`
` rArr x^(2) - 6x - 7 lt 0`
` rArr (x+1)(x-7) lt 0`
` rArr -1 lt x lt 7`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise Exercise 1.2|9 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise Exercise 1.3|16 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise Example 1.10|1 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE PUBLICATION|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

Solve (1//2)^(x^(2)-2x) lt 1//2 .

The number of integral values of x satisfying the inequality (3/4)^(6x+10-x^2)<(27)/(64) is _____

Solve (1/2)^(x^(6)-2x^(4)) lt 2^((x)^(2)) .

Solve (x(3-4x)(x+1))/(2x-5)lt 0

Solve (x^2-4)sqrt(x^2 -1) lt 0.

Solve (2x+3)/(x^(2)+x-12) lt (1)/(2) .

Solve (3x-2)lt=1/2

3(1-x) lt 2(x+4)

Solve (2)/(x) lt 3 .

Solve log_(2).(x-4)/(2x+5) lt 1 .