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

AI Generated Solution

To solve the equation \( 4^{\log_{9} x} - 6x^{\log_{9} 2} + 2^{\log_{3} 27} = 0 \), we will follow these steps: ### Step 1: Rewrite the equation using properties of logarithms and exponents We can express \( 4 \) as \( 2^2 \) and \( 27 \) as \( 3^3 \): \[ 4^{\log_{9} x} = (2^2)^{\log_{9} x} = 2^{2 \log_{9} x} = 2^{\log_{9} x^2} \] \[ ...
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise ILLUSTRATION 1.52|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise ILLUSTRATION 1.53|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise ILLUSTRATION 1.50|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

Solve x^(log_(4) x)=2^(3(log_(4)x+3) .

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

Solve : log_(2)(4-x)=4-log_(2)(-2-x)

Solve log_4(log_3x)-log_(1//4)(log_(1//3)y)=0 and x^2+y^2=17/4 .

Solve log_(4)(x-1)= log_(2) (x-3) .

Solve : log_(x^(2)16+log_(2x)64=3 .

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

The value 'x' satisfying the equation, 4^(log_(9)3)+9^(log_(2)4)=10^(log_(x)83)is ____

Solve (x^(log_(10)3))^(2) - (3^(log_(10)x)) - 2 = 0 .

Solve 1/4 x ^(log_(2)sqrtx)=(2*x^(log_(2)x))^(1/4).

CENGAGE ENGLISH-LOGARITHM AND ITS PROPERTIES-ILLUSTRATION 1.51
  1. Solve 4^(log(9)x)-6x^(log(9)2)+2^(log(3)27)=0.

    Text Solution

    |