Home
Class 12
MATHS
Solve (x^(log(10)3))^(2) - (3^(log(10)x)...

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

Text Solution

Verified by Experts

The correct Answer is:
` x = 10^(log_(3^(2)))`
Let `(x^(log_(10)3))=(3^(log_(10)x))=t`
Therefore, the given equation is
` t^(2) - t-2=0 or (t-2)(t+1) =0 `
` rArr t = 2" "("as t =- 1 is not possible")`
`rArr(3^(log_(10)x)) = 2`
` or log_(10)x = log_(3) 2`
` or x = 10^(log_(3)2)`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.5|13 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.6|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.3|16 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 x^(log_(3)x)=9

Solve: |x-1|^((log)_(10)x)^2-(log)_(10)x^2=|x-1|^3

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

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

Solve: ((1/2)^(log(10)a^2) +2>3/(2^((log)_(10)(-a))))

Solve log_x(x^2-1)<=0

Solve log_(10)(x^(2)-2x-2) le 0 .

Solve log_(3)(x-2) le 2 .

Solve : (log)_((x+3))(x^2-x)<1