Home
Class 12
MATHS
Solve 4^(log(9)x)-6x^(log(9)2)+2^(log(3)...

Solve `4^(log_(9)x)-6x^(log_(9)2)+2^(log_(3)27)=0`.

Text Solution

Verified by Experts

Given equation is
`(2^(log_(9^(x))))^(2) - 6(2^(log_(9^(x))))+27^(log_(3^(2)))=0`
Let` 2^(log_(9^(x)))=y," we get "y^(2)-6y+8=0`
` rArr y = 4 or 2`
If ` 2^(log_(9^(x))= 2^(2)`
` rArr log_(9)x = 2`
` rArr x = 81`
If ` 2^(log_(9^(x)))=2^(1)`
` rArr log_(9)x= 1`
` rArr x = 9`
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

The number of solutions set of the equation 4^(log_(9)x)-6.x^(log_(9)2)+2^(log_(3)27)=0 is

Solve :2(log)_(3)x-4(log)_(x)27 1)

Solve :6(log_(x)2-log_(4)x)+7=0

Solve (log_(3)x)(log_(5)9)- log_x 25 + log_(3) 2 = log_(3) 54 .

Solve :log_(4)(log_(3)(log_(2)x))=0

Solve 3^((log_(9)x)^(2)-9/2log_(9)x+5)= 3 sqrt3.

Solve: (log)_(2)(4.3^(x)-6)-(log)_(2)(9^(x)-6)=1

Solve: log_(9)x+log_(x)9+log_(x)x+log_(9)9=0

If 4^(log_(9)(3))+9^(log_(2)(4))=10^(log_(x)(83)) then x=

Solve log_(3)x+log_(9)x+log_(27)x=(11)/(2)