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 for x.x^(log_(10)x+2)=10^(log_(10)x+2)

Find 'x' satisfying the equation 4^(log_(10) x + 1) - 6^(log_(10)x) - 2.3 ^(log_(10)x^(2) + 2) = 0 .

Solve |x-1|^((log_(10)x)^(2)-log_(10)x^(2))=|x-1|^(3)

Solve :log_(0.3)(x^(2)-x+1)>0

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

x^(3log_(10)^(3)x)-(2)/(3)log_(10)x=100(10)^((3)/(2))

Solve for x: a) (log_(10)(x-3))/(log_(10)(x^(2)-21)) = 1/2 b) log(log x)+log(logx^(3)-2)= 0, where base of log is 10. c) log_(x)2. log_(2x)2 = log_(4x)2 d) 5^(logx)+5x^(log5)=3(a gt 0), where base of log is 3. e) If 9^(1+logx)-3^(1+logx)-210=0 , where base of log is 3.

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

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

Solve: log_(0.5)(3-x)/(x+2)<0